l and m are two parallel lines intersected by another pair of parallel lines p and q (see Fig. 7.19). Show that ΔABC ≅ ΔCDA.

Solution:

Given: l || m and p || q

To Prove: ΔABC ≅ ΔCDA.

We can show both the triangles are congruent by using ASA congruency criterion

In ΔABC and ΔCDA,

∠BAC = ∠DCA (Alternate interior angles, as p and q are parallel lines)

AC = CA (Common)

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

∴ ΔABC ≅ ΔCDA (By ASA congruence rule)

☛ Check: NCERT Solutions Class 9 Maths Chapter 7

Video Solution:

l and m are two parallel lines intersected by another pair of parallel lines p and q (see Fig. 7.19). Show that ΔABC ≅ ΔCDA.

NCERT Maths Solutions Class 9 Chapter 7 Exercise 7.1 Question 4

Summary:

If l and m are two parallel lines intersected by another pair of parallel lines p and q, then ΔABC ≅ ΔCDA using ASA conguence.

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