Find your Math Personality!

Find your Math Personality!

# 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.

**☛ Related Questions:**

- Line l is the bisector of an angle ∠A and B is any point on l. BP and BQ are perpendiculars from B to the arms of ∠A (see the given figure). Show that:i) ΔAPB ≅ ΔAQBii) BP = BQ or B is equidistant from the arms of ∠A
- In the given figure, AC = AE, AB = AD and ∠BAD = ∠EAC. Show that BC = DE.
- AB is a line segment and P is its mid-point. D and E are points on the same side of AB such that Show that ∠BAD = ∠ABE and ∠EPA = ∠DPB (See the given figure). i) ΔDAP ≅ ΔEBP ii) AD = BE
- In right triangle ABC, right angled at C, M is the mid-point of hypotenuse AB. C is joined to M and produced to a point D such that DM = CM. Point D is joined to point B (see the given figure). Show that:i) ΔAMC ≅ ΔBMDii) ∠DBC is a right angle.iii) ΔDBC ≅ ΔACBiv) CM = 1/2 AB

Math worksheets and

visual curriculum

visual curriculum