Question

In the given figure O is the midpoint of BD. Find how many pairs of congruent Triangles are there. Also state the Criterion of congruency

Answer 1

(i) Δ AOB ≅ Δ AOD

(ii) Δ BOC ≅ Δ DOC and

(iii) Δ ABC ≅ Δ ACD

Criteria for congruency is SSS criteria.

Step-by-step explanation:

See the attached diagram.

In the given diagram, there are three pairs of congruent triangles:

(i) Δ AOB ≅ Δ AOD

(ii) Δ BOC ≅ Δ DOC and

(iii) Δ ABC ≅ Δ ACD

In all the pairs of congruent triangles given above the criteria for the congruency is Side-Side-Side i.e. SSS criteria.

For example, Δ AOB ≅ Δ AOD, because

(a) AB = AD (Given)

(b) AO is the common side, and

(c) BO = OD {As O is the midpoint of BD}

So, applying the SSS criteria Δ AOB ≅ Δ AOD. (Answer)