Question

l and m are two parallel lines interested by another pair of parallel lines p and q ( see Dig. 7.19)show that ABC= CDA.

Answer 1

if the parallel m and p parallel q them angle ABC = angle CDA(alternative angles)

Answer 2

Given : l and m are parallel lines intersected by another pair of parallel lines P and Q

To prove : triangle ABC is congruent to triangle CDA

Proof : In ΔABC and ΔCDA

∠BCA = ∠DAC (Alternate interior angles)

∠BAC = ∠DCA (Alternate interior angles)

AC = AC (common)

Therefore, By ASA congruence,

By ASA congruence,ΔABC ≅ ΔCDA

Proved