School name

(A) the identification method of triangle congruence

1, as shown in figure: 2 of △ABC and △DEF, as shown in figure: △ABC and △DEF.

∵∵

∴△ABC≌△DEF()∴△ABC≌△DEF()

3. As shown in the figure: △ABC and △ def; 4. As shown in the figure: △ABC and △DEF.

∵∵

∴△ABC≌△DEF()∴△ABC≌△DEF()

5. As shown in the figure: in Rt△ABC and Rt△DEF, ∞ _ _ _ _ = ∞ _ _ = 90.

∵

∴Rt△ABC≌Rt△DEF()

(B) the characteristics of congruent triangles

∫△ABC?△DEF

∴AB=,AC=BC=，

(The corresponding side of congruent triangles)

∠A=，∠B=，∠C =；

(The corresponding side of congruent triangles)

(3) Fill in the blanks

1, given that △ Abd△ CDB, AB and CD are corresponding edges, then AD=, ∠ A =;

2. As shown in the figure, it is known that △ Abe △ DCE, AE=2cm, BE= 1.5cm.

∠A = 25∠B = 48； Then DE=cm, EC=cm,

∠C= degree; ∠D= degree;

3. As shown in the figure, △ ABC△ DBC, ∠A=800, ∠ABC=300.

Then ∠DCB= degrees;

(Question 4) Question 5

4. As shown in the figure, if △ ABC △ ade, the corresponding angle is:

There are corresponding edges (just write a pair each);

5. As shown in the figure, it is known that ∠ ABC = ∠ def and AB = de, and it is necessary to explain △ ABC △ def.

(1) If it is based on "SAS", you must add another condition:

(2) If it is based on "ASA", another condition that must be added is;

(3) If it is based on "AAS", a condition must be added:

6. As shown in the figure, the congruent triangle ABCD in the parallelogram.

Yes;

7. As shown in the figure, ∠ cab = ∠ DBA is known. To make △ ABC △ worse, just

One additional condition is;

(Just fill in one condition you think is appropriate)

8. According to the following known conditions, add another condition to make △ABD and △ACE in the following figure congruent;

( 1),,;

(2),,;

(3),,;

9. As shown in the figure, AC = BD, BC = AD. Explain why △ABC and △ BC=AD are congruent.

Proof: in △ABC and △BAD,

∵

∴△ABC≌△BAD()

10, as shown in the figure, CE=DE, EA=EB, CA=DB, verification: △ ABC △ bad.

Prove ∵CE=DE, EA=EB.

∴________=________

In △ABC and △BAD. ,

∵

∴△ABC≌△BAD.()

(4) Answer questions:

1, as shown in the figure, known as AC=AB, ∠1= ∠ 2; Verification: BD=CE

2. Point M is the midpoint of the bottom AB of the isosceles trapezoid ABCD. Are△ △AMD and△ △BMC congruent? Why?

3. It is known: as shown in the figure, AB‖CD, AB = CD, BE ‖ DF;

Verification: be = df

(choose to do the problem)

4. In △ ABC, ∠BAC is an acute angle, AB=AC, AD and BE are high, and intersect at H point, AE = BE.

(1) verification: AH = 2BD；;

(2) If ∠BAC is changed to obtuse angle, and other conditions remain unchanged, is the above conclusion still valid? If yes, please prove it; If not, please explain the reasons;