First, multiple-choice questions:
1. The following statement is wrong ()
A. The corresponding sides of congruent triangles are equal. The angles of congruent triangles are equal.
C. The circumference of congruent triangles is equal. Congruent triangles is equal in area.
2. Point O is a point within △ABC, the distances from point O to three sides are equal, and ∠ BAC = 60, then ∠BOC has a degree ().
A.60 B.90 C. 120 D. 150
3. As shown in the figure, it is known that △ABC and △DEF are congruent triangles, so the isometric line in the figure is ().
A. 1 b group 2 c group 3d group 4 group
4. As shown in the figure, △ ABC △ def, AC∨DF, then the angle corresponding to ∠C is ().
A. France B. France C. AEF D.
5. As shown in the figure, in △AB=AC, AB=AC, D and E are on BC, AD = AE, BD = CE.
If ∠ bad = 30 and ∠ DAE = 50, ∠BAC is ().
A. 130 b . 120 c . 1 10d . 100
6. As shown in the figure, in △ABD and △ACE, AB = AC and AD = AE. To prove △ Abd △ ace, the supplementary condition is ().
A.∠B =∠C B .∠D =∠E C .∠DAE =∠BAC D .∠CAD =∠DAC
7. As shown in the figure, AD and BC intersect at point O, and it is known that ∠ A = ∠A=∠C, according to "ASA"
To prove △ AOB △ COD, one more condition needs to be added: ()
A.AB=CD B. AO=CO C.BO=DO D.∠ABO=∠CDO
8. As shown in the figure, given AB = AD, it is still uncertain whether △ ABC△ ADC is () after adding one of the following conditions.
A.CB = CD B .∠BAC =∠DAC c .∠BCA =∠DCA D .∠B =∠D = 90
9. As shown in the figure, the intersection o of AC and BD, and OA = OC, OB = OD, then the congruent triangles logarithm in the figure has ().
A.2 to B.3 to C.4 to D.6.
10. As shown in the figure, in △ABC, ∠ A = 36, ∠ C = 72, and BD is the bisector of ∠ABC, then the degree of ∠BDC is ().
A.36 B. 48 C. 60 D. 72
1 1. As shown in the figure, P is the point of bisector of ∠BAC, PM⊥AB is in M, and PN⊥AC is in N, and the following conclusions are obtained: (1) PM = PN;
⑵AM = AN； ⑶ The areas of △ APM and △APN are equal; (4) ∠ Pan+∠ APM = 90。 Among them, the correct conclusion is ()
A. 1 .
12. Draw the following conclusions: ① An acute angle and a hypotenuse correspond to the congruence of two right-angled triangles; ② Two isosceles triangles with equal top and bottom angles are congruent; ③ Two isosceles triangles with equal top and bottom angles are congruent; ④ A triangle with two equal angles is congruent. The correct number is ().
1。
Second, fill in the blanks:
13. In △ABC, ∠ b = ∠ c, if one angle in the triangle congruent with △ABC is 92, then △ABC has three angles.
The degree of is ∠ a =; ∠B =； ∠C=。
14. Given △ABC △ dEF, BC = EF = 6, the area of △ ABC is 18, and the height of the ef side is.
15. As shown in the figure, at △ABC, ∠ BAC = 90, AB = AC, F is the upper point of BC, the extension line of BD⊥AF passing through AF is at D, CE⊥AF is at E, given CE = 5 and BD = 2, then ED =.
16. As shown in the figure, if ∠ DC = EC = ∠ A = 90, BE⊥AC is at point B, DC = EC, Be = 200px, then AB+AD =.
17. As shown in the figure, in the right triangle ABC, ∠ BAC = 90, AB = AC, respectively passing through B and C are the perpendicular lines of the straight line passing through point A, if BD = 75px, CE = 100px, then DE =.
On 18. △ABC, ∠ C = 90, and AD divides ∠BAC equally. Given BC = 200px, BD = 125px, the distance from point D to AB is.
19. Various conditions for judging the congruence of two right-angled triangles: (1) an acute angle and an edge; (2) Both parties are equal; (3) The two acute angles are equal. The condition that two right triangles are congruent is.
20. Rotate the right triangle ABC clockwise around the right vertex C to the position of △ dec, if point E is on the side of AB and ∠ DCB = 160, ∠ AED =.
Third, answer questions:
2 1. A graph is congruent before and after translation, folding and rotation. Write the corresponding edges and corners according to the following congruent triangles.
(1) △ ABC △ CDA corresponds to an edge of and a corresponding angle of;
(2) △ AOB △ Doc, corresponding edge is, corresponding angle is;
(3) △ AOC △ BOD, the corresponding edge is, and the corresponding angle is;
(4) △ ace △ BDF, the corresponding edge is and the corresponding angle is.
22. As shown in the figure, in △AB=DC and △DCB, AC and BD intersect at point O, AB=DC and AC = BD.
Proof: △ ABC △ DCB.
23. AB = AD, AC = AE, ∠ 1 = ∠ 2,
Verification: (1) △ ABC △ ade ∠ 2 ∠ b = ∠ d.