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CBSE Class 9 Mathematics Question 4 of 21

Triangles — Question 4

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Question 4

l and m are two parallel lines intersected by another pair of parallel lines p and q. Show that Δ ABC ≅ Δ CDA.

l and m are two parallel lines intersected by another pair of parallel lines p and q. Show that Δ ABC ≅ Δ CDA. NCERT Class 9 Mathematics CBSE Solutions.
Answer

Given :

l || m and p || q

In Δ ABC and Δ CDA,

⇒ ∠BAC = ∠DCA (Alternate interior angles are equal)

⇒ AC = CA (Common side)

⇒ ∠BCA = ∠DAC (Alternate interior angles are equal)

∴ Δ ABC ≅ Δ CDA (By A.S.A. congruence rule)

Hence, proved that Δ ABC ≅ Δ CDA.