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:

l//m and p//q

therefore

ABCD is a parallelogram

since opp angles are equal

angle ABC = angle CDA

Answer 2

Step-by-step explanation:

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Solution:

It is given that p q and l m

To prove:

Triangles ABC and CDA are similar i.e. ΔABC ΔCDA

Proof:

Consider the ΔABC and ΔCDA,

(i) BCA = DAC and BAC = DCA Since they are alternate interior angles

(ii) AC = CA as it is the common arm

So, by ASA congruency criterion, triangle ABC triangle CDA.

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