Question

3. In the given figure, two parallel lines I and m
are intersected by two parallel lines p and q.
Show that A ABC = ACDA.
8
C​

Answer 1

Answer:

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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Answer 2

Step-by-step explanation:

ANSWER

In △ABC and △CDA

∠BAC=∠DCA (Alternate interior angles, as p∥q)

AC=CA (Common)

∠BCA=∠DAC (Alternate interior angles, as l∥m)

∴△ABC≅△CDA (By ASA congruence rule)