Question

What additional information is needed to prove the triangles are congruent by ASA?

Answer 1

To prove that two triangles with three congruent, corresponding angles are congruent, you would need to have at least one set of corresponding sides that are also congruent. You could then use ASA or AAS congruence theorems or rigid transformations to prove congruence.

Explanation:

Answer 2

The additional information that needed is m∠ABD = m∠CDB ⇒ C

Explanation:

In the given figure

Triangles ADB and CBD are congruent by ASA under these conditions

1. m∠ADB = m∠CBD
2. DB = BD ⇒ the side joining the congruent angles
3. m∠ABD = m∠CDB

Let us see the given to find the correct answer

∵ ∠ADB and ∠CBD have the same mark

∴ m∠ADB = m∠CBD ⇒ (1) given

∵ Side DB is a common side in the two triangles

∴ DB = BD ⇒ (2) given

∵ ∠ABD and ∠CDB are the angles at the end of BD

∴ m∠ABD must equal m∠CDB ⇒ (3) to prove the congruency using ASA

∴ The additional information that needed is m∠ABD = m∠CDB