Mathematics quadrilateral examination questions in the second volume of the eighth grade
First, multiple-choice questions (4 points for each small question, 40 points for * * *)
1, in the quadrilateral ABCD, o is the intersection of diagonal lines, and the condition for judging that this quadrilateral is the lower square is ().
A.AC=BD，AD CD b . AD∨BC，？ A=？ C
C.AO=BO=OC=DO，AB=BC D. AO=CO，BO=DO，AB=BC
2. A quadrilateral () surrounded by four bisectors of a rectangle.
A. it must be a square. B. it is a rectangle. C. it can only be a parallelogram.
3. Cut a rectangle with a width of 2cm from the square iron sheet, and the remaining area is 48 cm 2, so the original area of the square iron sheet is ().
A. Length 8 cm, width 64 cm, height 8 cm, width 64 cm and height
4. As shown in the figure, D and E are the midpoint of AC side and BC side of △ABC respectively. Fold the triangle along DE so that point C falls on point P on AB side. What if? CDE=48？ ,? APD is equal to ()
A.42? B. 48？ C. 52？ D. 58？
5. As shown in figure □ABCD, diagonal AC and BD intersect at point O. If AC= 12, BD= 10 and AB=m, the range of m is ().
A. 1 & lt； m & lt 1 1 b . 2 & lt； m & lt22
C. 10 & lt； m & lt 12d . 5 & lt； M< six
6. As shown in the figure, in the rectangular ABCD, AB=3, AD=4, point P is on AB, and PE? AC, PF in e? If BD is in F, then PE+PF is equal to ()
A.B. C. D。
7. As shown below, extend one side BC of the square ABCD to E to make CE=AC, and connect AE to CD at F, then? The degree of AFC is ()
A. 1 12.5? B. 120？
C. 122.5? D. 135？
8. As shown in the figure, e is any point in the parallelogram. If S □ABCD=8, the area of the shaded part in the figure is ().
A.3 B. 4 C. 5 D. 6
9. As shown in the figure, the area at □ABCD is 12, points E and F are on AC, AE=EF=FC, then the area of △BEF is ().
A.6 B. 4 C. 3 D. 2
10, the diagonal AC and BD of quadrilateral ABCD intersect at point O, and the conclusion is as follows:
& lt 1 & gt； AB = BC:& lt； 2 & gt？ DAB=90？ :& lt3 & gtBO=DO，AO = CO:& lt； 4> rectangular ABCD& lt5> diamond ABCD& lt6> square ABCD, then the following inference is incorrect ().
A.B. C. D。
Fill in the blanks (5 points for each small question, 20 points for * * *)
1 1, as shown in the figure, the side length of the square ABCD is 1, and E, F, G and H are the midpoint of each side, so the area of the shaded part in the figure is ().
12, as shown in the figure, consists of five squares with side length of 1? Ten? A graphic with symmetrical fonts, what about in the picture? The degree of BAC is ().
13 As shown in the figure, in □ABCD, e and f are the midpoint of AD and BC respectively, and AC intersects with BE and d F at G and H respectively. The conclusions are as follows: ① Be = DF; ②AG = GH = HC； ③: ④ s △ Abe = 3s △ age, where the correct one is ().
14, as shown in the figure, is a square pattern inlaid by four identical small rectangles and a small square. It is known that the pattern has an area of 49 and the small square has an area of 4. If x and y are used to represent the length of both sides of a small rectangle (x >；; Y), please observe the pattern and write three equations expressed by x and y.
Third, answer questions.
15, as shown in the figure, in the rectangular ABCD,? The bisector of BAD intersects BC at point e, o is the intersection of diagonal AC and BD, and? CAE= 15？
(1) Prove that △AOB is an equilateral triangle: (2) Find? BOE degree.
16. Known: As shown in the figure, in □ABCD, BE. CE split equally? ABC？ E, BE= 12cm and CE=5cm on BCD and AD. Find the perimeter and area of □ABCD.
If two equal-width rectangles overlap in 17 and (1) graphs, what special quadrilateral is the overlapping quadrilateral ABCD? No proof is needed.
(2) If there are two congruent rectangles in (1), the rectangles are 8cm long and 4cm wide, and they do not overlap completely when they overlap together, try to find the minimum area and the maximum area of the overlapping quadrilateral ABCD, and please draw a schematic diagram of the situation when the area is the largest.
18, known: in △ABC,? C=90？ ,? A=30？ BC=3cm, there is a bug P next to AB, which climbs from A to B along AB at the speed of 1cm/ s, and PE after passing P? BC, PF in e? AC in f, find the functional relationship between the perimeter y(cm) of (1) rectangular PECF and the crawling time t (seconds), and the range of independent variables;
(2) How long does the bug crawl? Quadrilateral PECF is a square.
19, (1) as shown in the figure, □ABCD is known. Try three methods and divide it into two parts with equal area. (Keep drawing traces, don't write)
What general conclusions can you draw from the above methods?
(2) Problem solving: When the two brothers split up, a parallelogram field ABCD originally contracted by * * * should now be divided equally. Because there is a P well in this field, as shown in the figure, in order to facilitate the brothers to use this well, the two brothers are in trouble when they divide it. Clever, can you help them solve this problem? (Keep drawing traces, don't write)
20. As shown in the figure, in △ABC, AB=BC, BD is the center line, the intersection point D is DE∨BC, the intersection point A is AE∨BD, and AE and DE intersect at E. It is proved that the quadrilateral ADBE is rectangular.
2 1, as shown in the figure, in △ABC, point O is a moving point on the side of AC, and the intersection point O is a straight line MN∨BC, which can be crossed by MN? The bisector of BCA angle is at point E, crossing? The bisector of the outer corner of BCA is at point F.
(1) verification: EO = FO
(2) When the point O moves to where, the quadrilateral AECF is a rectangle? And prove your conclusion.
22. Known in △ABC, BC >；; AC, moving point d rotates counterclockwise around vertex a of △ABC, and AD=BC connects DC. The midpoints E and F of AB and DC are straight lines, and the straight line EF intersects with the straight lines AD and BC at points M and N respectively.
(1) As shown in figure 1, when point D rotates to the extension line of BC, point N coincides with point F, and the midpoint H of AC is taken to connect he and HF. According to the theorem of triangle midline and the properties of parallel lines, can we draw a conclusion? AMF=？ BNE (no proof required)
(2) When point D rotates to the position shown in Figure 2 or Figure 3,? AMF and? What is the quantitative relationship of BNE? Please write your guesses separately and choose any kind of proof.
23. As shown in the figure, in quadrilateral ABCD, AC=6, BD=8, AC? BD, connecting the midpoints of the sides of the quadrilateral ABCD in turn to obtain quadrilateral A1B1C1D1; Then connect the midpoints of the sides of quadrilateral A1B1C1D1in turn to get quadrilateral A 2B 2C 2D 2, and so on to get quadrilateral A NBNC ND N.
(1) It is proved that quadrilateral A1b1c1d1is a rectangle;
(2) Carefully explore and solve the following problems: (fill in the blanks) ① The area of quadrilateral A1B1C1D1is _ _ _ _ _ _ _ _ _ _ _ _ _ _ _; (2) The area of quadrilateral AnBnCnDn is _ _ _ _ _ (expressed by algebraic expression containing n); ③ The perimeter of the quadrilateral A5B5C5D5 is _ _ _ _ _ _ _.
Reference answers to quadrilateral questions of mathematics in the second volume of the eighth grade.
C
Test analysis:
analyse
This topic is to examine the method of judging a square. There are two ways to judge whether a quadrilateral is a square: ① it is a rectangle first, and then a group of adjacent sides are equal; Explain that it is a diamond, and then explain that it has a right angle.
According to the judgment of the square, the quadrilateral whose diagonal lines are vertically bisected and equal is analyzed and the final answer is obtained.
explain
Solution: A. Because the conditions of AD∨CD and AD=CD cannot be established, it cannot be judged as a square;
B. No, it can only be judged as a parallelogram;
C. yes;
D. no, it can only be judged as diamonds.
So choose C.
A
Test analysis:
analyse
This topic examines the nature and judgment of rectangle, square, isosceles right triangle and congruent triangles. Mastering the nature and reasoning of rectangle is the key to solve the problem. It is proved that the quadrilateral GMON is a rectangle from the nature of the rectangle and the bisector of the angle, and then it is proved that △DOC, △AMD and △BNC are isosceles right triangles, so that OD=OC, △ AMD △ BNC, NC=DM and OM=ON are obtained.
explain
Solution: As shown in the figure, the quadrilateral ABCD is a rectangle.
Bad =? CBA=？ BCD=？ ADC=90？ ，AD=BC，
∫AF, BE is the bisector of the inner corner of a rectangle.
DAM=？ BAF=？ ABE=？ CBE=45？ .
1=? 2=90? .
Similar:? MON=？ OMG=90？ ,
? The quadrilateral GMON is a rectangle.
And ∵AF, BE, DK and CJ are bisectors of corners of rectangular ABCD,
? △DOC, △AMD and △BNC are isosceles right triangles.
? OD=OC，
At △AMD and △BNC,
? △AMD?△BNC(AAS)，
? NC=DM，
? NC-OC=DM-OD，
Which means OM=ON,
? The rectangle GMON is a square.
So choose a.
D
Test analysis:
analyse
This question examines the application of quadratic equation in one variable, and it is the key to solve the problem to find the key descriptors and the listed equations with accurate equivalence. In the process of solving problems, we should pay attention to choosing values according to practical significance.
Let the side length of a square be xcm, according to? The remaining area is 48cm2? The rest of the graph is a rectangle. The length of a rectangle is the side length of a square and the width is x-2. According to the area formula of rectangle, equations can be listed and solved.
explain
Solution: Let the side length of the square be xcm, and according to the meaning of the question, x(x-2)=48.
The solution is x 1=-6 (truncation), x2=8,
So the area of square iron sheet is 8? 8=64 (square centimeter).
So choose D.
B
Test analysis:
analyse
This topic examines the positional relationship of the midline theorem in triangles and applies the knowledge of triangle folding transformation. The key to solve this problem is to understand that the graphics after folding transformation are exactly the same as the original graphics. PDE=？ CDE and de ∑AB are obtained from the median theorem, then? CDE=？ DAP, further supply? APD=？ CDE。
Solution: ∫△PED is transformed from △CED.
? △PED?△CED
CDE=？ EDP=48？ ,
∫DE is the center line of △ABC,
? DE∑AB，
APD=？ CDE=48？ ,
So choose B.
A
Test analysis:
analyse
This topic examines the understanding and mastery of knowledge points such as the nature of parallelogram and the theorem of triangular trilateral relationship, and finds OA and OB, and then obtains OA-OB.