Classification of Mathematics Test Questions in 2007-Projection and Similarity

(Wuhu City, 2007) As shown in the figure, at △ABC, AD⊥BC and CE⊥AB, the vertical feet are D and E respectively, and AD and CE intersect at H point. If EH=EB=3 and AE=4, the length of CH is ().

A. 1 B. 2 C. 3 D.4

(Shaoguan City, 2007) As shown in figure 1, if CD is the height on the hypotenuse of Rt△ABC, the logarithm of similar triangles in the figure is ().

A.0 to B. 1 to C. 2 to D.3.

(Shaoguan City, 2007) Xiaoming plays with equilateral triangular wooden frames in the sun. The projection formed by equilateral triangular wooden frame on the ground can't be ().

(Shi Yan, 2007) As shown in the figure, point O is a point outside △ABC. Taking points A', B' and C' on rays OA, OB and OC respectively, and connecting A'B', B'C'And C' a' in this way, is the △A'B'C' obtained similar to △ABC? Prove your conclusion.

(Nanchang, 2007) In China, China, China, China, China, China, China and Nanchang, in order to make them similar, it is necessary to add a condition (write only one situation).

(Binzhou, 2007) As shown in figure 1 1, in harmony, …

(1) Determine whether these two triangles are similar? And explain why?

(2) Can you draw an auxiliary line in each of these two triangles so that the two triangles are similar to each other? Prove your conclusion.

(Jingzhou City, 2007) As shown in the figure, in the isosceles trapezoid ABCD, AD‖BC, Guo C is CE‖AB, and P is a point in the trapezoid ABCD, which connects BP and extends the intersection points CD to F, Ce to E, and then connects PC. Known BP = PC, the following conclusion is wrong ().

A.∠ 1 =∠2 b .∠2 =∠E . c .△PFC∽△PCE d .△EFC∽△ECB。

(Jingmen City, 2007) The light from the light bulb (regarded as a point) directly above the round table illuminates the desktop and forms a shadow on the ground (pictured). Given the diameter of the desktop, the desktop is 1 m from the ground. If the light bulb is 3 meters from the ground, the area of the shadow on the ground is ().

A. square meters

C. square meters

(Taian, 2007) As shown in the figure, the middle,, is the height of the side, which is a moving point on the side (not coincident with it), and the vertical feet are respectively.

(1) Verification:;

(2) Is it perpendicular to? If vertical, please give proof; If it is not vertical, please explain why;

(3) When is it an isosceles right triangle? And explain why.

(Taian, 2007) As shown in the figure, in the square, it is the midpoint, which is the last point.

Draw the following conclusions: ①, ②,

③, ④ The number of correct conclusions is ()

A. 1

C.3 D.4

As shown in the figure, given that AB‖CD, AD and BC intersect at point P, AB=4, CD=7 and AD= 10, the length of AP is equal to

A.B. C. D。

(Anhui, 2007) As shown in the figure, DE is the point on the side of BC and AB of △ABC, the perimeters of △ABD and △ACD are equal, and the perimeters of △CAE and △CBE are equal. Let BC=a, AC=b, AB = C.

(1) Find the length of AE and BD;

(2) If ∠ BAC = 90, and the area of △ABC is S, then verify: S=AE? Bachelor of science

Changzhou City (2007) is as shown in the figure. It can be seen that,,,

Then,,.

Zunyi City (2007) as shown in the figure, a point divides a line segment into two line segments, and if, then this line segment is divided by the golden section of the point, and the ratio of the sum is called the golden section ratio, which is ().

A.B. C. D。

Zunyi City (2007) is shown as two overlapping right triangles. One of the right triangles translates along the direction. If,,, the shaded part in the figure is.

(Wuxi, 2007) Wang wants to make a ladder as shown in the figure 1. The ladder has eight parallel steps, and the distance between every two adjacent steps is equal. The lengths of the top step and the bottom step of the ladder are known. When making these steps, the carpenter intercepted the boards that were longer than the pedals to ensure that the two outer ends of each step had a length of 4 cm. In this way, the pedal can be fixed. At present, there are plates with a length of 2. 1m on the market, which can be used to make ladder pedals (the width and thickness of the plates just meet the requirements for making ladder pedals). How many boards does Wang need to buy to make these pedals? Please explain the reason. (regardless of the wear and tear of the saw seam)

(Xiantao City, Qianjiang City, 2007) As shown in Figure ①, OABC is a rectangular piece of paper placed in a plane rectangular coordinate system, with O as the origin, point A on the positive semi-axis of the shaft, and point C on the positive semi-axis of the shaft, with OA=5 and OC=4.

(1) Take a point D on the edge of OC, fold the paper along AD, make the point O fall on the point E on the edge of BC, and find the coordinates of the two points D and E;

(2) As shown in Figure ②, if there is a moving point P (which is not coincident with A and E) on AE, it will move from point A to point E in the AE direction at a uniform speed of 1 unit length per second, and the moving time will be seconds. The parallel lines passing through point P intersect at point M as ED, and the parallel lines passing through point M intersect at point N as AE, so as to find the functional relationship between the area S of quadrilateral PMNE and time. What is the value of S? What is the maximum value?

(3) Under the condition of (2), when the value is what, the triangles with vertices A, M and E are isosceles triangles, and the coordinates of the corresponding time point M are obtained.

(Xiantao City, Qianjiang City, 2007) As shown in the figure, AB is ⊙O in diameter, AD is tangent to ⊙O at point A, BC‖OD crosses ⊙O at point C after passing through point B, and connecting OC, AC and AC crosses ⊙ o at point E. 。

(1) Verification: △ COE ∽△ ABC;

(2) If AB=2 and AD=, find the area of the shaded part in the figure.

(Xiantao City, Qianjiang City, 2007) Xiaohua found his shadow length on the ground 6 meters away from the street lamp. If Xiaohua's height is 1.6 meters, the height of the street lamp from the ground is meters.

(Jinan City, 2007) As shown in the figure, in the plane rectangular coordinate system, it is a right triangle, and the coordinates of the points are,,, respectively.

(1) Find the function expression of a straight line passing through this point;

(2) Find a point on the axis, connect it to make it similar (excluding congruence), and find the coordinates of the point;

(3) Under the condition of (2), if you move points, connections and settings on and respectively, ask whether there is such similarity, and if so, ask its value; If it does not exist, please explain why.

Xiangtan City (2007) as shown in the figure, two equal-length steel bars cross to form a caliper, which can be used to measure the width of the working inner groove. If set and measured, the width of the inner groove is equal to ().

A.B.

C.d . `

(Luzhou, 2007) It is known that △ABC is similar to △, and △ABC is similar to △.

Delta area ratio

1: 1 B. 1:2

C. 1:4

(Foshan City, 2007) In China,

A point moves in a straight line so that

(counterclockwise).

(1) As shown in figure 1, if a point moves on a line segment, it will be crossed.

① Verification:;

② When it is an isosceles triangle, find the length.

(2)① As shown in Figure 2, if a point moves on the extension line of, and the reverse extension line of, intersects with the extension line of, does one point make it an isosceles triangle? If it exists, write down the positions of all points; If it does not exist, please briefly explain the reason;

(2) As shown in Figure 3, if a point moves on the reverse extension line of, is there a point that makes it an isosceles triangle? If it exists, write down the positions of all points; If it does not exist, please briefly explain why.

(Foshan, 2007) As shown in the picture, there is a burning candle (no matter how long or short) on the ground. If a person moves from wall to wall, his projection length on the wall will decrease with his distance from the wall (fill in "bigger", "smaller" or "unchanged").

(Lianyungang, 2007) The right picture is a schematic cross-sectional view of a valley, with a width of, measured from both sides of the valley with a ruler (the two rulers intersect at right angles),,, (points are on the same horizontal line), indicating that the depth of the valley is.

(Huanggang City, 2007) As shown in the figure, in the plane rectangular coordinate system, the quadrilateral ABCO is a diamond, and ∠ AOC = 60, and the coordinate of point B is point P. Starting from point C, point B moves to point B at the speed of 1 unit length per second on the line segment CB, and the straight line PQ intersects with OB at point D one second later.

(1) Find the number of times ∠AOB and the length of line OA;

(2) Find the analytical formula of parabola passing through points A, B and C;

(3) when, find the value of t at this time and the analytical formula of straight line PQ;

(4) When a is what value, are triangles with vertices of O, P, Q and D similar? When a is what value, are there triangles of O, P, Q and D similar? Please give your conclusion and prove it.

At a certain moment (Yancheng, 2007), the shadow length of the square of 165cm is 55cm. At this time, Xiaoling measured the shadow length of the flagpole at the same place as 5m, so the height of the flagpole was m.

(Ningbo City, Zhejiang Province, 2007) As shown in the figure, there is an iron tower AB at the top of the slope, where B is the midpoint of CD and CD is horizontal. In the sun, Tayingde stayed on the slope. It is known that the tower base CD= 12 m, the tower shadow length DE= 18 m, and the heights of Xiaoming and Xiaohua are both 1.6m, which are the same.

(a) 24m (b) 22m (c) 20m (d)18m

(Ningbo City, Zhejiang Province, 2007) As shown in the figure, the rectangular ABCD is folded in half, and the crease is MN. Rectangular DMNC is similar to rectangular ABCD, and AB = 4 is known.

(1) Find the length of AD.

(2) Find the similarity ratio between rectangular DMNC and rectangular ABCD.

(Yangzhou City, 2007) As shown in the figure, in a rectangle, cm, cm (). At the same time, the moving point starts from this point and moves forward at the speed of cm/s. When the straight lines are vertical and cross, the point stops moving when it reaches the end point. Set the moving time to seconds.

(1) If cm, seconds, then _ _ _ _ _ cm.

(2) If cm, find the time and work, and find their similarity ratio;

(3) If there is a moment in the process of movement that makes the area of the trapezoid equal to the area of the trapezoid, the required value range;

(4) Is there such a rectangle? Is there a moment when the trapezoid, trapezoid and trapezoid area are all equal during the movement? The value of, if it exists; If it does not exist, please explain why.

(Shuangbai County, 2007) As shown in the figure, in the plane rectangular coordinates, the quadrilateral OABC is an isosceles trapezoid, CB‖OA, OA=7, AB=4, ∠ COA = 60, and point P is the moving point on the X axis, which does not coincide with point 0 and point A. Connect CP and cross point P to make PD cross AB.

(1) Find the coordinates of point B;

(2) When the point P moves to what position, △OCP is an isosceles triangle, and the coordinates of the point P at this time are found;

(3) When point P moves, let ∠CPD=∠OAB, and find the coordinates of point P at this time.

(Jining, 2007) As shown in the figure, firstly, fold a rectangular ABCD paper in half, set the crease as MN, and then fold point B on the crease line to get △ABE. The folded paper passes through point B to make point D overlap with straight line AD, and a crease PQ is obtained.

(1) verification: △ pbe ∽△ qab;

(2) Do you think △PBE and △ Pei are similar? If the proofs are similar, if the supplements are similar, please explain the reasons;

(3) If straight EB is used for origami, can point A be superimposed on straight EC? Why?

(Wenzhou, 2007) On Sunday, Nana Ogawa and his father went for a walk in the park. Nana Ogawa's height is160cm, his shadow length in the sun is 80cm, and his father's height is180cm. At this point, his father's shadow length is _ _ _ _ cm.

As shown in the figure of Qingliu County (2007), in a 4×4 square grid, the vertices of △ABC and △DEF are all on the vertices of a square with a side length of 1.

(1) Fill in the blank: ∠ ABC = _ _ _ _ _ _; BC = _ _ _ _ _ _ _ _

(2) Judge whether △ABC and △DEF are similar, and explain the reasons.

(Yantai, 2007) As shown in the figure, if A, B, C, P, Q, A, B, C and D are all grid points in grid paper, in order to make △PQR∽△ABC, the point R should be between the four points A, B, C and D.

Motion Picture Association of America.

China Center for Disease Control and Prevention.

Yantai (2007) as shown in the figure, the specifications of each picture on the film are 3.5cm× 3.5cm, and the projection screen specifications are as follows.

2 m×2 m, if the light source S of the projector is 2 0 cm away from the film, then the light source S is projected at a distance of meters from the screen.

Images fill the whole screen.

(Meizhou City, 2007) As shown in figure 1, Liang Xiao walks under a street lamp at night and in Liang Xiao.

In the process of getting there, his shadow was on the ground ()

A. gradually shorten

C. First get shorter and then get longer. D. First get longer and then get shorter.

Meizhou City (2007) connects Shanghai, Hongkong and Taiwan Province Province in the Geographic Atlas of China.

Form a triangle and measure the distance between them with a ruler as shown in Figure 3.

The direct flight distance from Taiwan Province Province to Shanghai is about 1286 km, so the plane left Taiwan Province.

The flight distance from Hong Kong to Shanghai is about 1000 km.

(Jinhua City, 2007) After learning projection, Xiao Ming and Xiao Ying measured the height of a street lamp with their own shadow length under the light to explore the changing law of shadow length. For example, the length of the shadow BC of Xiaoming (AB) with a height of 1.6m is 3m, while Xiaoying (EH) is directly below the street lamp bulb at H point, and HB=6m is measured. (1) Please draw the light that forms the shadow in the picture and determine the position g of the street lamp bulb; (2) Find the vertical height GH of the street lamp bulb; (3) If Xiaoming walks along BH to Xiaoying (point H), when Xiaoming walks to the midpoint of BH B 1, find the length of his shadow b1c1; When Xiaoming continues to walk the rest of the way to B2, find the length of the shadow B2C2. When Xiaoming continues to walk the rest of the way to B3, … According to this law, when Xiaoming walks the rest of the way to Bn, the length of his shadow BnCn is m (directly expressed by the algebraic expression of n).

( 1)

(2) In terms of meaning,

，，(m)。

(3) , ,

Let the length be, then the solution is: (m), that is, (m).

Similarly, the solution is (m).

In order to carry forward the spirit of Lei Feng, a middle school in Wuhan (2007) is going to build a 2-meter-high statue of Lei Feng on campus, and collect design plans from all teachers and students. Students in Xiao Bing have consulted relevant materials and learned that the golden section number is often used in the design of human statues. As shown in the figure, the plan of Lei Feng's human figure designed by Xiao Bing students according to the golden section number, in which the design height (accurate to 0.0 1m, reference data: ≈ 1.4 14, ≈ 1.732, ≈2.236) of the lower part of Lei Feng's human figure is ().

A, 0.62m b, 0.76m c,1.24m d,1.62m.

(Wuhan in 2007) You must have played on the seesaw! The picture shows Xiaoming and Xiaogang playing on the seesaw. The crossbar rotates up and down around its midpoint O, and the column OC is vertical to the ground. When one side touches the ground, the other side rises to the highest point. Q: What is the quantitative relationship between the maximum heights AA' and BB' that two people rise in the process of rotating the crossbar up and down? Why?

The extracurricular activity group of Class 9 (1) in Huaihua City (2007) measured the height of the flagpole in the school with a benchmark, and calculated the height of the flagpole by knowing the height of the flagpole, the horizontal distance between the flagpole and the flagpole, the height between people's eyes and the ground, and the horizontal distance between people and the flagpole.

(Huzhou, 2007) It is known that in △ABC, D is a point on AC, with AD as one side, making ∠ADE and AB intersect at E point, △ADE∽△ABC, where the corresponding side of AD is AB. (Requirements: Draw with a ruler, keep traces of drawing, and don't write and prove).

(Shaoyang, 2007) As shown in Figure (3), the midpoint and the antipoint are the midpoint of the side length, so the ratio to the area is ().

A.B. C. D。

(Shaoyang, 2007) As shown in the figure (1 1), the straight line intersects the axis and the axis at points respectively. Rotate the angle () clockwise around this point to obtain.

(1) Find the coordinates of this point;

(2) When a point falls on a straight line, the overlapping part of the straight line and the sum of the intersections is (Figure ①). Verification:

(3) Apart from the situation in (2), is there any similar overlap? If yes, please indicate the degree of rotation angle; If it does not exist, please explain the reason;

(4) When (Figure ②), and intersect at a point and intersect at a point respectively, find the area of the overlapping part of and (that is, quadrangle).

(Changsha, 2007) As shown in the figure, in the middle,,, is the last moving point (not coincident with it), and the extension line consisting of,, passes through this point, with an area of.

(1) Verification:;

(2) Find the expressed function expression and write the value range;

(3) Where to move, there is a maximum, and what is the maximum?

(Fuzhou, 2007) As shown in the figure, AOB = 45, points passing through OA with distances of 1, 3, 5, 7, 9, 1 1, … intersect with OB, and a group of black trapeziums are obtained and marked, with areas of. Observe the rule in the figure, and find the area of the10th black trapezoid = _ _ _ _ _ _ _ _ _. 76

As shown in the figure, take the vertex A of rectangular ABCD as the origin, the straight line where AD is located as the X axis, and the straight line where AB is located as the Y axis, and establish a plane rectangular coordinate system. The coordinates of point D are (8,0), point B is (0,6), point F moves on the diagonal AC (point F does not coincide with points A and C), the intersection point F is perpendicular to the X axis and Y axis, and the vertical feet are G and E. Let the area of quadrilateral BCFE be, the area of quadrilateral CDGF be and the area of △AFG be.

(1) Try to judge the relationship between them and prove it;

(2) When: = 1: 3, find the coordinates of point F;

(3) As shown in the figure, under the condition of (2), translate △AEF along the straight line where the diagonal AC is located, and get △ A ′ E ′ F ′, and the points A ′ and F ′ are always on the straight line AC. Is there such a point E', the ratio of the distance from E' to X axis to Y axis is 5: 4? If it exists, request the coordinates of point E'; If it does not exist, please explain why.

( 1)S 1 = S2

Proof: as shown in figure 10, ∫fe⊥ axis, FG⊥ axis, ∠ bad = 90.

∴ Quadrilateral AEFG is a rectangle.

∴ AE = GF，EF = AG。

∴ S△AEF = S△AFG, in the same way S△ABC = S△ACD.

∴ S△ABC-S△AEF = S△ACD-S△AFG。 That is, S 1 = S2.

(2)∫fg‖CD，∴ △AFG ∽ △ACD。

∴ .

∴ FG = CD，AG = AD。

∵ CD = BA = 6，AD = BC = 8，∴ FG = 3，AG = 4。 ∴ F(3，4).

(3) The solution1:∫△ a ′ e ′ f ′ is obtained by translating △AEF along a straight line AC.

∴ E'A'= E A = 3，E'F'= E F = 4。 ① as shown in figure 1 1- 1.

The ratio of the distance from the E' point to the axis is 5: 4. If the point E' is in the first quadrant,

∴ let e' (4,5) and >; 0 ,

Extend the horizontal axis of E'A' to m, and get a' m = 5-3 and am = 4.

∠∠E′=∠A′M A = 90°，∠E′A′F′=∠M A′A，

∴△ e' a' f' ∴△ ma' a, get it.

∴ .∴ =，e′(6，)。

② As shown in figure 1 1-2.

The distance ratio from the E' point to the axis is 5: 4,

If point e' is in the second quadrant, let e' (-4,5) and >; 0,

NA = 4，A'N = 3-5，

In the same way, △ a ′ f ′ e ′∞△ a ′ an can be obtained.

∴ , .

∴ a =，∴e′(，)。

③ As shown in figure 1 1-3.

The distance ratio from the E' point to the axis is 5: 4,

If point e' is in the third quadrant, let E'( -4,-5) and >; 0.

Extend the intersection of e'f' at point p, and get AP = 5 and P'= 4-4.

Similarly, you can get △A'E'F'∽△A P F', you can get,

= (unwilling to give up)

There is no point E' in the third quadrant.

④ Point E' cannot be in the fourth quadrant.

∴ There are E' coordinates that meet the conditions, namely (6,) and (,).

Solution 2: As shown in figure 1 1-4, ∫△ a ′ e ′ f ′ is translated from △AEF along a straight line AC, and the two points A ′ and F ′ are always on the straight line AC.

The point E' moves on a straight line L that passes through the point E (0 0,3) and is parallel to the straight line AC.

The analytical formula of ∫ linear AC is,

The analytical formula of ∴ straight line L is.

According to the meaning of the question, the coordinates of the point e' that meets the conditions are set to (4,5) or (-4,5) or (-4,5), where >; 0 .

Point e' is on the straight line l, ∴ or or

Solve (don't give up). ∴ E'(6,) or e' (,).

∴ There are E' coordinates that meet the conditions, namely (6,) and (,).

Solution 3:

∫Δa ′ e ′ f ′ is obtained by translating Δ △AEF along a straight line AC, and the two points A ′ and F ′ are always on the straight line AC.

The point E' moves on a straight line L that passes through the point E (0 0,3) and is parallel to the straight line AC.

The analytical formula of ∵ straight line AC is, and the analytical formula of ∴ straight line L is.

Let e' point be (,) ∵ The ratio of the distance from e' point to axis is 5: 4, ∴.

(1) When it is the same as the symbol, the solution is ∴ e ′ (6,7.5).

② When sum is different symbols, we can get ∴e'' (,).

∴ There are E' coordinates that meet the conditions, which are (6,) and (,) respectively.

(Hangzhou, 2005) As shown in the figure, it belongs to () to enlarge graphics with a magnifying glass.

A. similarity transformation B. translation transformation C. symmetry transformation D. rotation transformation

(Hangzhou, 2005) As shown in the figure, it is known that the vertical lines of, and intersect at points. Have the following conclusions:

(1) ray is bisector;

② isosceles triangle;

③ ;

④ .

(1) What are the correct conclusions?

(2) choose a conclusion that you think is correct to prove.

Weihai (2007) shows that the side length of each small square in the square grid is 1. Try to find the degree.

(Taizhou, 2007) As shown in the figure, a quadrilateral is a rectangular piece of paper placed in a plane rectangular coordinate system, with points on the axis and points on the axis. Fold the edge so that the point falls on the point of the edge. Folding is known.

(1) and similar? Please explain the reasons;

(2) Find the coordinates of the intersection of the straight line and the axis;

(3) Is there a straight line passing through this point, so that the triangle surrounded by straight line, straight line and axis is similar to the triangle surrounded by straight line, straight line and axis? If it exists, please write its analytical formula directly and draw the corresponding straight line; If it does not exist, please explain why.

(Shanghai, 2007) As shown in Figure 2, it is a point on the extension line of parallelogram, which is connected with and intersects with this point. Please write a pair of similar triangles in the picture without auxiliary lines.

Yiyang City (2007) In a math activity class, Teacher Li led the students to measure the height of the teaching building. In the sunshine, the BA of Huang Li's classmate BC, whose height is 1.65m, is measured as 1. 1m, and the DF of the teaching building DE is12.1m..

(1) Please draw the projection DF of the teaching building DE in the sun in Figure 7.

(2) Please calculate the height of the teaching building DE (accurate to 0. 1m) according to the measured data.

Deyang (2007) as shown in the figure, the known isosceles area is _ _ _ _ _ _ _ _.

As shown in the figure (lengshuitan area in 2007), it is known that in △ABC, BE=8, AC=4, ∠ C = 60, EF‖BC, and points E, F and D are on AB, AC and BC respectively (point E does not coincide with points A and B), connecting ED and DF.

(1) Find the functional relationship between Y and X, and write the range of the independent variable X;

(2) When point F is in which position on AC, the area of △EFD is the largest?

(3) Question: Is there a point D on BC that makes △EFD an isosceles right triangle? If it exists, find the length of EF; If it does not exist, please briefly explain the reason;

(lengshuitan area in 2007) As shown in the figure, in △ABC, D and E are the midpoint of AB and AC respectively, F is a point on the extension line of BC, and DF bisects CE in G, so the area ratio of △CFG to △BFD is _ _ _ _ _.

(Bazhong, 2007) As shown in Figure 6, it is obtained by multiplying the vertical and horizontal coordinates of each vertex by the vertical and horizontal coordinates of the corresponding vertex.

① Draw the obtained relationship (4 points) ② Guess the sum and explain the reason (5 points).

(Zhoushan, Zhejiang, 2007) As shown in the figure, it is known that AB=AC, ∠A=36o, and the midline MN of AB intersects with AC at point D and with AB at point M, and there are four conclusions as follows:

① Is ray BD the bisector of ABC? ②△BCD is an isosceles triangle;

③△ABC∽△BCD； ④△AMD?△BCD。

(1) What are the correct conclusions?

(2) choose a conclusion that you think is correct to prove.

(Yongzhou, 2007) As shown in the figure, add the condition: _ _ _ _ _ _, and then △ABC∽△ADE.

12. (Qingdao, 2007) The diagram shows the principle of pinhole imaging. According to the size marked in the figure, if the height of the object AB is 36cm, then the height of the image CD it forms in the cassette should be cm.

Answer: 16

Analysis: (Qingdao, 2007) This topic mainly investigates the projection problem. Because light is a straight line, it is often necessary to construct a triangle when solving problems about projection and line of sight, and then look for similar triangles in the topic, and use the properties of triangle and similar triangles to solve the problem. The projection problem is mainly solved by similar triangles's knowledge. From the title, we can find that △AOB∽△COD can get the proportional relationship and CD = 16.

Neijiang (2007) as shown in figure (12), in △ABC, AB = 5, BC = 3, AC = 4, the moving point E (not coincident with points A and C) is on the side of AC, and EF‖AB intersects BC at point F. 。

(1) When the area of △ECF is equal to the area of quadrilateral EABF, find the length of CE;

(2) When the perimeter of △ECF is equal to the perimeter of quadrilateral EABF, find the length of CE;

(3) Is there a point P on 3)AB that makes △EFP an isosceles right triangle? If it does not exist, please briefly explain the reason; If it exists, request the length of EF.

(Zaozhuang, 2007) As shown in the figure, the CD is a flat mirror, and the light emitted from point A is reflected by point E on the CD and irradiated to point B. Let the incident angle be A (the incident angle is equal to the reflection angle), AC⊥CD and BD⊥CD, and the vertical feet are C and D respectively. If AC=3, BD = 6, CD = 65438.

(A) (B) (C) (D)