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# ABC is an isosceles triangle with AB = AC. Draw AP ⊥ BC to show that ∠B = ∠C.

**Solution:**

Let's construct a diagram according to the given question.

In triangles APB and APC,

∠APB = ∠APC (Each 90°)

AB = AC (Since ABC is an isosceles triangle)

AP = AP (Common)

ΔAPB ≅ ΔAPC (Using RHS congruence rule)

Thus, ∠B = ∠C (CPCT)

**☛ Check: **NCERT Solutions Class 9 Maths Chapter 7

**Video Solution:**

## ABC is an isosceles triangle with AB = AC. Draw AP ⊥ BC to show that ∠B = ∠C

NCERT Maths Solutions Class 9 Chapter 7 Exercise 7.3 Question 5

**Summary:**

If ABC is an isosceles triangle with AB = AC and AP ⊥ BC, then ∠B = ∠C.

**☛ Related Questions:**

- ΔABC and ΔDBC are two isosceles triangles on the same base BC and vertices A and D are on the same side of BC (see the given figure). If AD is extended to intersect BC at P, show thati) ΔABD ≅ ΔACDii) ΔABP ≅ ΔACPiii) AP bisects ∠A as well as ∠Div) AP is the perpendicular bisector of BC.
- AD is an altitude of an isosceles triangle ABC in which AB = AC.Show that i) AD bisects BC ii) AD bisects ∠A.
- Two sides AB and BC and median AM of one triangle ABC are respectively equal to sides PQ and QR and median PN of ΔPQR (see Fig. 7.40). Show that:(i) Δ ABM ≅ Δ PQN(ii) Δ ABC ≅ Δ PQR
- BE and CF are two equal altitudes of a triangle ABC. Using RHS congruence rule, prove that the triangle ABC is isosceles.

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