We know that the two triangles corresponding to the two sides and the opposite corners of one side are not necessarily congruent. Under what circumstances will they be congruent? (1) Read and prove: When both triangles are right triangles, they are obviously congruent If the two triangles are obtuse angle triangles, their congruence can be proved When these two triangles are acute triangles, they are also congruent, which can be proved as follows: Known: as shown in the figure, △ ABC, △ a1b1c1 are obtuse angle triangles, ab = A1B1, BC = b1c1, ∠ C = ∠ C1 Verification: △ BCD ≌ b1c1d1 (please complete the following certification process) It is proved that when passing through points B and B1 respectively, BD ⊥ CA is made at D, and b1d1 ⊥ c1a1 is made at D1, then ∠ BDC = ∠ b1d1c1 = 90 degree ∵BC=B1C1,∠C=∠C1 ∴△ABC≌△A1B1C1 ∴BD=B1D1. ______________________ ______________________ . I just want you to explain why a diagonal on both sides can be congruent Submit the satisfactory additional before 10 o'clock today

We know that the two triangles corresponding to the two sides and the opposite corners of one side are not necessarily congruent. Under what circumstances will they be congruent? (1) Read and prove: When both triangles are right triangles, they are obviously congruent If the two triangles are obtuse angle triangles, their congruence can be proved When these two triangles are acute triangles, they are also congruent, which can be proved as follows: Known: as shown in the figure, △ ABC, △ a1b1c1 are obtuse angle triangles, ab = A1B1, BC = b1c1, ∠ C = ∠ C1 Verification: △ BCD ≌ b1c1d1 (please complete the following certification process) It is proved that when passing through points B and B1 respectively, BD ⊥ CA is made at D, and b1d1 ⊥ c1a1 is made at D1, then ∠ BDC = ∠ b1d1c1 = 90 degree ∵BC=B1C1,∠C=∠C1 ∴△ABC≌△A1B1C1 ∴BD=B1D1. ______________________ ______________________ . I just want you to explain why a diagonal on both sides can be congruent Submit the satisfactory additional before 10 o'clock today

When both triangles are right triangles, they are obviously congruent
If the two triangles are obtuse angle triangles, their congruence can be proved
When these two triangles are acute triangles, they are also congruent, which can be proved as follows:
Known: as shown in the figure, △ ABC, △ a1b1c1 are obtuse angle triangles, ab = A1B1, BC = b1c1, ∠ C = ∠ C1
Verification: △ BCD ≌ b1c1d1
(please complete the following certification process)
It is proved that when passing through points B and B1 respectively, BD ⊥ CA is made at D, and b1d1 ⊥ c1a1 is made at D1, then ∠ BDC = ∠ b1d1c1 = 90 degree
∵BC=B1C1,∠C=∠C1
∴△ABC≌△A1B1C1
∴BD=B1D1.

Proof: two triangles with two corners and the height on the edge between the two corners correspond to the same congruence

It is known that in △ ABC, △ a1b1c1, ≌ △ a1b1c1, ≌, BD and b1d1 are the heights on the sides of AC and a1c1 respectively, BD = b1d1. It is proved that ≌ △ a1b1c1, ≌, BD and b1d1 are the heights on the sides of AC and a1c1 respectively, ≌, ≌, ≌, BD = b1d1, ≌, ab = AAS and ≌, ab = 90 ° in △ abd and △ a1b1d1= A1B1，∴△ABC≌△A1B1C1（AAS）．

The square of (2a + 3b) - (2a + 3b) (3b-2a) where a = 1 and B = - 2 are first simplified and then evaluated

（2a+3b）2-（2a+3b）（3b-2a）=（2a+3b）[（2a+3b)-(3b-2a)]=（2a+3b）(4a)=4(2-6)=-16