Question

In the given figure, two parallel line l and m are intersected by two parallel lines p and q.
Show that ΔABC ≅ ΔCDA.

Answer 1

Answer:

Given:-l is parallel to m

p is parallel to q

To prove:-∆ABC is congruent to ∆ CDA

Proof:- In ∆ ABC and ∆CDA

angle BAC= angle ACD( alternate angles)

AC=AC ( common)

angle BCA=angle DAC( alternate angles)

By ASA congruence,

∆ABC is congruent to ∆ 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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