L and m are two parallel lines intersected by

Asked by admin @ 17/08/2021 in Math viewed by 324 People

"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"

Answered by admin @ 17/08/2021

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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L and m are two parallel lines intersected by

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