Question

in the adjoining figure l and m are two Parallel Lines intersected by another pair of parallel lines p and q show that triangle ABC is congruent to triangle CDA

Answer 1

given,
l || m
p || q

to prove: ∆ ABC is congruent ∆CDA
proof: in ∆ABC and ∆CDA
angle ACB = angle CAD ( alt. int. angles)
AC= AC (common)
angle BAC = angle DCA(alt. int angles)
∆ABC is congruent ∆CDA by ASA congruencey rule


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Answer 2

In ΔABC and ΔCDA,

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

AC = CA (Common)

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

∴ ΔABC ≅ ΔCDA (By ASA congruence rule)