Eighth grade mathematics volume I chapter 13 axisymmetric unit test questions
(Time:120min, full mark:120min)
First, multiple-choice questions (3 points for each small question, 30 points for * * *)
1. The following figure is not axisymmetric ()
2. Given that point P(3, -2) and point Q are symmetrical about X, the coordinate of point Q is ().
A.(-3，2) B.(-3，-2) C.(3，2) D.(3，-2)
3. It is known that the circumference of isosceles △ABC is 18 cm, and BC=8 cm. If △ABC and △A? b？ c？ Congruence, then △A? b？ c？ The waistline of is equal to ()
A.8 cm B.2 cm or 8 cm C.5 cm D.8 cm or 5 cm.
4. The following statement is true ()
A the bisectors of the height, midline and angle of an isosceles triangle coincide with each other. B. Two isosceles triangles with equal vertex angles are congruent.
C. The two base angles of an isosceles triangle are equal. One side of an isosceles triangle cannot be twice as big as the other.
5.(20 14? Dandong) as shown in the figure, in △ABC, AB=AC,? A=40？ The perpendicular line of AB crosses AB at point D, crosses AC at point E, and connects BE, then? The degree of CBE is ()
Point 70? B.80？ C.40？ D.30？
6. As shown in the figure, in △ABC, AB=AC,? A=36？ , BD, CE? ABC and? The bisectors of ACB, BD and CE intersect at point F, then the isosceles triangle in the figure has ().
a6 b . 7 c . 8d . 9
Figure 5), Figure 6), Figure 7), Figure 8)
7. As shown in the figure, in △ABC,? A=90？ ,? C=30？ ，AD？ BC in d, BE in? The bisector of ABC, the intersection of AD and P. If AP=2, the length of AC is ().
A.2 B.4 C.6 D.8
8. As shown in the figure, in △ABC,? ACB= 100？ AC=AE, BC=BD, then? The degree of DCE is ()
.20 caliber? B.25？ C.30？ D.40？
9. The height of one waist of an isosceles triangle is higher than half the length of the other side of the triangle, and its vertex angle is equal to ()
.30 caliber? B.30？ Or 150? C. 120？ Or 150? D. 120？ ,30? Or 150?
10. As shown in the figure, in △ABC,? A=90？ , AB=20 cm, AC= 12 cm, point P starts from point B and moves to point A at a speed of 3 cm per second, while point Q starts from point A and moves to point C at a speed of 2 cm per second. When one moving point reaches the end point, another moving point stops moving. △ When △APQ is an isosceles triangle, the movement time is ().
A 2.5 seconds B 3 seconds C 3.5 seconds D 4 seconds.
,No. 10),No. 13),No. 14)
Fill in the blanks (3 points for each small question, 24 points for * * *)
1 1. The five-pointed star on the national flag is an axisymmetric figure with _ _ _ _ _ symmetry axes.
12. The internal angle of an isosceles triangle is 68? , the degree of the other two internal angles is _ _ _ _ _.
13. As shown in the figure, there is a bottom angle of 35? An isosceles triangular piece of paper, now passing through a point on the bottom edge, is cut in the direction perpendicular to the bottom edge and divided into two parts: a triangle and a quadrilateral, so the degree of the largest angle in the quadrilateral is _ _ _ _ _ _ _ _.
14. As shown in the figure, in Rt△ABC,? B=90？ , AB=3 cm, S△ABC=6 cm2, fold △ABC to make point C coincide with point A and get a crease DE, then the circumference of △ABE is equal to _ _ _ _ _ cm.
15. As shown in the figure, in ABC, ABC= 120? , AB=BC, and the midpoint m of AB is MN? AB, alternating with AC at point n, if AC= 12 cm, then CN = _ _ _ _ _ _
16. in the plane rectangular coordinate system xOy, it is known that point P (2 2,2), point Q*** are on the y axis, and △PQO is an isosceles triangle, then there are _ _ _ _ _ _ _ points that meet the conditions.
,No. 15),No. 17)
,No. 18)
17. As shown in the figure, it is known that △ABC is an equilateral triangle, point O is any point on BC, OE and OF are perpendicular to both sides respectively, and the height of the equilateral triangle is 1, then the value of OE+OF is _ _ _ _ _.
18. The figure is a hexagon composed of nine equilateral triangles. If the side length of the small equilateral triangle in the middle is known as a, the circumference of the hexagon is _ _ _ _ _ _ _.
Iii. Answering questions (***66 points)
19.(8 points) As shown in the figure, in the triangular piece of paper ABC,? A=65？ ,? B=80？ Fold a corner of a piece of paper so that point C falls within △ABC, if? 1=20? , beg? 2 degrees.
20.(8 points) As shown in the figure, Village A and Village B are on the same side of a small river, and a water plant will be built along the river to supply water to the two villages.
(1) If the distance between the waterworks and the two villages is equal, where should the site be selected?
(2) In order to save water pipe materials from waterworks to two villages, where should the site be selected? Please mark the location of the waterworks in the above two cases and keep the drawing traces.
2 1.(8 minutes) As shown in the figure, a ship sails due north at a speed of 20 nautical miles per hour, and the lighthouse C is measured to be 30? Direction, the ship sailed for 2 hours to reach B, and B measured that the lighthouse C was 60? Direction. How many nautical miles did the ship sail when it reached D just east of lighthouse C?
22.( 10/0) In a math class, Teacher Wang drew the following picture on the blackboard and wrote down four equations: ①AB=DC, ②BE=CE, ③? B=？ c，④？ BAE=？ CDE。
Ask students to choose two of these four equations as conditions, and deduce that △AED is an isosceles triangle. Please try your best to fulfill the requirements put forward by Mr. Wang and explain the reasons. Just write one. )
Known: _ _ _ _ _ _ _ _ _ _.
It is proved that △AED is an isosceles triangle.
Prove:
23.( 10) As shown in the figure, in the known isosceles Rt△OAB,? AOB=90？ , isosceles Rt△EOF,? EOF=90？ , connect AE, BF.
Verification: (1) AE = BF; (2)AE？ BF。
24.( 10) As shown in the figure, there are two islands A and B in the sea, which are measured at point E on the coastline PQ? AEP=74？ ,? BEQ=30？ , measured at point F? AFP=60？ ,? BFQ=60？ .
(1) Judge the quantitative relationship between AE and AB, and explain the reasons;
(2) Q? BAE degree
25.( 12 points) As shown in the figure, △ABC is an equilateral triangle, AE=CD, AD and BE intersect at point P, BQ? A D in q, PQ=3, PE= 1, and find the length of AD.
The eighth grade mathematics first volume chapter 13 axisymmetric unit detection volume reference answer.
1.C 2。 C 3。 D 4。 C 5。 D 6。 C 7。 C 8。 D 9。 D 10。 D 1 1.5 12.56？ ,56? Still 68? ,44? 13. 125? 14.715.8cm16.417.118.30a.
19. extend AE and BF to point d? A=65？ ,? B=80？ ，D= 180？ -80? -65? =35? ，C=35？ , again? 1=20? ,? CEF=？ DEF，？ 1+? CEF+？ DEF= 180？ ，CEF= 180？ -20? 2=80? ，CFE= 180？ -80? -35? =65? ,2= 180? -652=50?
20.( 1) As shown in Figure ①, point M is the demand; (2) As shown in Figure ②, point N is the demand.
2 1.∵? CAB=30？ ,? CBD=60？ ，BCA=？ CAB=30？ ,? AB=B C，？ BC=20？ 2=40 (nautical miles)? CDB=90？ ,? CBD=60？ ，DCB=30？ ,? BD= 12BC=20 (nautical mile)
22.∵? B=？ c，？ AEB=？ DEC，BE=CE，？ △ Abe△ ?△DCE, AE=DE，？ △AED is an isosceles triangle
23.( 1)∵Rt△OAB and Rt△EOF are isosceles right triangles. AO=OB，OE=OF，？ AOB=？ EOF=90？ ，AOB-？ EOB=？ EOF-？ Which is EOB? AOE=？ BOF？ △AEO?△BFO(SAS)，？ AE=BF (2) If AE passes through BF in D and OB in C, then? BCD=？ ACO, known as (1):? OAC=？ BDA OBF =？ AOB=90？ ,? AE？ novio
24.( 1)AE=AB, reason: ∵? BEF=30？ ,? AFE=60？ ，EOF=90？ ,∵? BFQ=60？ ,? BEF=30？ ，EBF=30？ ,? BF=EF，？ OE=OB, that is, AF bisects BE vertically,? AE = AB(2)∫？ AEP=74？ ，AE B= 180？ -74? -30? =76? ，BAE= 180？ -762=28?
25.∫△ABC is an equilateral triangle, BAC=? C=60？ , AB=AC, and AE = CD,? △ABE?△CAD(SAS)，ABE=？ CAD，BE=AD，∫？ BPQ=？ BAP+？ ABE=？ BAP+？ PAE=？ BAC=60？ And ∵BQ? PQ，AQB=90？ ，PBQ=30？ ,? PQ= 12PB，？ PB=2PQ=6，？ BE=PB+PE=6+ 1=7，？ AD=BE=