Question

"Question 4 l and m are two parallel lines intersected by another pair of parallel lines p and q (see the given figure). Show that ΔABC ≅ ΔCDA.

Class 9 - Math - Triangles Page 119"

Answer 1

Hope it helps...:): :)

Answer 2

ASA(angle side angle):

Two Triangles are congruent if two angles and the included side of One triangle are equal to two angles & the included side of the  other triangle.

Alternate angles:

When two lines are crossed by another line the pair of angles on opposite sides of the transversal is called alternate angles.

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Use the properties of a transversal intersecting two Parallel Lines i.e, interior angles are equal to each other, to show congruence of given Triangles.

 

Given,
l || m and p || q

To prove,
ΔABC ≅ ΔCDA

Proof,
In ΔABC and ΔCDA,
∠BCA = ∠DAC (Alternate interior angles as p||q)

AC = CA (Common)

∠BAC = ∠DCA (Alternate interior angles as l ||m)

Hence, ΔABC ≅ ΔCDA (by ASA congruence rule.)

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