Question

Fig. 7.18
I and m are two parallel lines intersected by
another pair of parallel lines p and q
(see Fig. 7.19). Show that A ABC=ACDA.
Fig. 7.19​

Answer 1

Step-by-step explanation:

Given: l Il m & p ll q

To prove: triangle ABC = triangle CDA

Proof: Taking I II m and AC is the transversal,

angle ACB = angle CAD (Alternate angles)

now p II q and AC is the transversal,

angle BAC = angle DCA. (Alternate angles)

In triangle ABC and triangle CDA,

angle ACB = angle CAD

AC = CA (Common)

angle BCA = angle DAC

ΔΑΒC = ΔCDA (ASA congruence rule)

Hence proved