Question

Which postulate or theorem can be used to prove that △ABD≅△CBD?

​ SSS Congruence Postulate ​
​ HL Congruence Theorem ​
​ ASA Congruence Postulate ​
​ SAS Congruence Postulate ​

Answer 1

Answer: SAS congruence postulate (choice D)

Note how AD = CD based on the double tickmarks along these segment lines. This is the first S in SAS. The A in SAS refers to the congruent angles ADB and BDC. The final S in SAS would be the shared side BD = BD. It's important to realize that the angles are between the pairs of congruent sides for each triangle. The order matters. If the angles weren't between the two sides, then you can't use SAS.

Answer 2

Answer: ​ SAS Congruence Postulate ​

Explanation:

• SAS Congruence Postulate ​ says that if two sides and a included angle of one triangle are congruent to corresponding two sides and a included angle of other triangle then the triangles are said to be congruent.

In the given figure , in △ABD and △CBD

i.e. AD= CD [Given]

∠ADB = ∠BDC [Given]

BD = BD [Reflexive property]

∴ by ​ SAS Congruence Postulate ​, we have

△ABD≅△CBD

Hence, the correct answer is ​SAS Congruence Postulate ​.