Class: Name: Seat Number:
First, multiple-choice questions (this big topic ***8 small questions, ***32 points)
1, only the following corresponding elements are equal, so it cannot be determined that two triangles are congruent ().
A. two angles and one side B. two sides and included angle C. three angles D. three sides
2. As shown in the figure: If △ Abe △ ACF, and AB=5, AE=2, the length of EC is ().
A: 2 B: 3 C: 5 D: 2.5
3, the following graphics, not axisymmetric graphics is ()
A. angle B. equilateral triangle C. line segment D. right triangle
4, an isosceles triangle with an internal angle of 50, then the degrees of the other two internal angles are ().
65 years, 65 years
C.50,50 d 65,65 or 50,80.
5. As shown in the figure, AD=AE, BD=CE, ∠ ADB = ∠ AEC = 100, ∠ BAE = 70, and the following conclusion is wrong ().
aδABE?δACD BδABD?δACE C∠DAE = 40d∠C = 30
6. If the lengths of three sides of an isosceles triangle are x, 6 and 8 respectively, then the length of x is ().
A.6b.8c. 10 d.a and b
7. In δ ABC and δ def, ∠B=∠E, ∠C=∠F, () You can't get δ ABC ≌ δ def by adding the following conditions.
A BC=EF B AB=DE C AC=DE D AC=DF
8. As shown in the figure: △ABC, ∠ C = 90, AC=BC, AD bisects ∠CAB through BC in D, and DE⊥AB in E, AB=6㎝, then the circumference of △DEB is ().
A: 6 ㎝ B: 4 ㎝ C: 10 ㎝ D: None of the above are correct.
2. Fill in the blanks. (This big question is ***8 small questions, ***32 points)
9. Two triangles that can completely overlap are called ().
10. The () of the isosceles triangle coincides with the () at the bottom.
1 1. As shown in Figure 9, all five corners of the five-pointed star are isosceles triangles with a vertex angle of 36, so the degree of ∠AMB is _ _ _ _ _ _ _. (Fill in options)
144 b . 120 c . 108d . 100
12. It is known that two sides of an isosceles triangle are 50px, and the circumference of 100px is _ _ _ _ _ _ _ _ _ _.
13. The isosceles triangle is an axisymmetric figure, and its axis of symmetry is
14, the coordinates of point M (-2, 1) which is symmetrical with respect to point n of X axis are _ _ _ _ _ _ _ _ _ _ _. Point.
The coordinates of the point Q where m (-2, 1) is symmetrical about the Y axis are _ _ _ _ _ _ _ _.
15. As shown in figure 14, it is known that AC = DB. In order to make △ ABC △ DCB, the supplementary condition is _ _ _ _ _ _ _ _ _ _ _ (only fill in one).
16, as shown in the figure: in △ABC, AD=AE, BD=EC, ∠ ADB = ∠ AEC = 105,
∠ b = 40, then∠ ∠CAE =；;
3. Drawing questions. (12)
17. Draw the axisymmetric figure of △ABC about X △ A1b1,and point out the vertex coordinates of △ A1b1.
.
18, as shown in the figure, there are two universities and two intersecting highways somewhere. In the picture, points M and N represent universities, while OA and OB represent expressways. Now it is planned to build a material warehouse. I hope the distance between the warehouse and the two universities is the same, and the distance between the two expressways is the same. Can you determine where warehouse P should be built? Please draw your design on the picture. (Draw with a ruler, don't write, leave traces of drawing)
4. Answer the questions. (44 points)
19, in isosceles △ABC, AB=AC, d is a point on AC, AD=BD=BC, and find the degrees of each angle of △ABC.
20. As shown in Figure (9), AE and BC intersect at point M, point F is on AM, BE∑CF, be = cf.
Prove that AM is the center line of △ABC.
20. known: as shown in the figure, it is the bisector of sum.
Verification:
2 1, (14 minutes) as shown in the figure: at △ABC, ∠ C = 90, AC=BC, the intersection point C is a straight line MN outside △ABC, AM⊥MN is in M, BN⊥MN is in N. (/kloc-0.
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