The proof that shows that ΔABD ≅ ΔCBD by ASA is explained below.
How to Prove that Two Triangles are Congruent by ASA?
We can prove that two triangles are congruent to each other by the ASA congruence theorem if we can show that two angles and one included side in one triangle is congruent to two corresponding angles and one corresponding side in the other triangle.
The proof that shows both triangles are congruent is explained below.
Statement Reason
1. AC ⊥ BD; DB bisects ∠ABC 1. Given
2. ∠ADB and ∠CDB are right 2. Definition of perpendicular.
angles, they are congruent.
3. ∠ABD ≅ ∠CBD 3. Definition of bisection
4. BD ≅ BD 4. Reflexive property
5. ΔABD ≅ ΔCBD 5. ASA
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