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CBSE Class 9 Mathematics Question 4 of 8

Triangles — Question 7

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Question 7

ABC is a right angled triangle in which ∠A = 90° and AB = AC. Find ∠B and ∠C.

Answer

Given :

AB = AC and ∠A = 90°

ABC is a right angled triangle in which ∠A = 90° and AB = AC. Find ∠B and ∠C. NCERT Class 9 Mathematics CBSE Solutions.

We know that,

Angles opposite to equal sides are also equal.

∠C = ∠B = x (let)

In Δ ABC,

⇒ ∠A + ∠B + ∠C = 180° (Angle sum property of a triangle)

⇒ 90° + ∠B + ∠C = 180°

⇒ 90° + x + x = 180° (From(1))

⇒ 2x = 180° - 90°

⇒ 2x = 90°

⇒ x = 90°2\dfrac{90°}{2}

⇒ x = 45°.

∴ ∠B = ∠C = 45°

Hence, ∠B = 45° and ∠C = 45°.

Triangles - Interactive Study Notes | Bright Tutorials
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Mathematics | TrianglesWeb Content • Interactive Notes

Triangles — Interactive Study Guide

Congruence Criteria at a Glance

CriterionYou NeedRemember
SAS2 sides + included angleAngle MUST be between the 2 sides
ASA2 angles + included sideSide MUST be between the 2 angles
AAS2 angles + any sideSide can be anywhere
SSS3 sidesAll three sides match
RHSRight angle + hypotenuse + sideONLY for right triangles
NEVER use AAA (only proves similarity) or SSA (ambiguous case)!

Proof Writing Pattern

Every congruence proof follows this pattern:

  1. Identify the two triangles to compare.
  2. List three pairs of equal elements (sides/angles) with reasons.
  3. State the criterion (SAS/ASA/AAS/SSS/RHS).
  4. Conclude congruence.
  5. Use CPCT for any further deduction.

Quick Self-Check

  1. In ΔABC, AB = AC. ∠B = 55°. Find ∠A. (∠C = 55°, ∠A = 70°)
  2. Can a triangle have sides 2, 3, 6? (No: 2+3=5 < 6, violates triangle inequality)
  3. In a triangle, the longest side is opposite to which angle? (The largest angle)

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