Q.1. In quadrilateral ACBD,AC = AD and AB bisects ∠ A(see Figure). Show that Δ ABC ≅ Δ ABD. What can you say about BC and BD?

Q.2. ABCD is a quadrilateral in which AD = BC and ∠DAB = ∠CBA (see Figure). Prove that

(i) Δ ABD ≅ Δ BAC

(ii) BD = AC

(iii) ∠ABD = ∠BAC.

Q.3. AD and BC are equal perpendiculars to a Line segment AB (see Figure). Show that CD bisects AB.

Ans:

Q.4. l and m are two parallel lines intersected by another pair of parallel lines p and q (see Figure). Show that ΔABC ≅ ΔCDA.

Q.5. 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 Figure). Show that:

(i) Δ APB ≅ Δ AQB

(ii) BP = BQ or B is equidistant from the arms of ∠A.

Q.6. In Figure, AC = AE, AB = AD and ∠BAD = ∠EAC. Show that BC = DE.

Q.7. AB is a line segment and P is its mid-point. D and E are points on the same side of AB such that ∠ BAD = ∠ ABE and ∠ EPA = ∠ DPB (see Figure). Show that

(i) Δ DAP ≅ Δ EBP

(ii) AD = BE

Q.8. 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 Figure). Show that:

(i) Δ AMC ≅ Δ BMD

(ii) ∠ DBC is a right angle.

(iii) Δ DBC ≅ Δ ACB

(iv) CM = $\frac{1}{2}$AB

NCERT Solutions For Class 9 Maths Chapter 7, Triangles (All Exercises)