Example 1 - Chapter 7 Class 9 - Triangles
In Fig. , OA = OB and OD = OC. Show that
(i) ∆ AOD ≅ ∆ BOC
Given:
OA = OB ...(1)
and OD = OC ...(2)
To prove: ΔAOD ≅ ΔBOC
Proof:
Line CD & AB intersect.
∠ AOD = ∠ BOC (Vertically opposite angles) ...(3)
In ∆ AOD and ∆ BOC,
OA = OB (From (1))
∠ AOD = ∠ BOC (From (3))
OD = OC (From (2))
So, Δ AOD ≅ Δ BOC (SAS Congruence Rule)
Example 1
In Fig. , OA = OB and OD = OC. Show that
(ii) AD ∥ BC.
Δ AOD ≅ Δ BOC (From 1st part)
∠ OAD = ∠ OBC (CPCT)
But ∠ OAD & ∠ OBC and these form a pair of alternate angles
If a transversal intersects two lines such that pair of alternate interior angles is equal, then lines are parallel.
Therefore, AD ∥ BC.

Made by

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.