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3 Equal Lines and Angles in Triangle

May 30, 2024 2025-05-30 0:31

Geometry-Mensuration

CAT / Geometry Mensuration / QUANT / Question Bank

3 Equal Lines and Angles in Triangle

May 30, 2024

CAT Geometry Concept – Triangle Medians & Angle

Table of Contents

📐 Concept: 3 Equal Lines and Angles in Triangle

Let triangle $△ A B C$ have point $D$ as a point on $B C$ .

Now, if $B D = A D = A C$ , then triangle has special symmetry.

From the triangle:

$A D = B D = D C$ implies triangle is divided into isosceles components
Use of angle algebra can help break this down

Triangle Median Angle Breakdown

🧪 CAT 2006 Question on Geometry

Q. In triangle $△ A B C$ , point $D$ is a point on $B C$ . If $B D = A D = A C$ and $∠ D A C = 96^{\circ}$ , then what is $∠ C$ ?

CAT 2006 Geometry Question Diagram

🔽 Show Answer & Step-by-Step Solution

Given:

$A D = A C$
$D$ is midpoint of $B C$
$∠ D A C = 96^{\circ}$

Since $A D = A C$ , triangle $△ A D C$ is isosceles.

Let $∠ D B C = ∠ x$ , then $∠ D A C = x$ and the external angle becomes:

$∠ D A C + ∠ C A B = 96^{\circ} \Rightarrow 2 x = 96^{\circ} \Rightarrow x = 32^{\circ}$

Now, use this to find angle $∠ C = 2 x = 64^{\circ}$

CAT 2006 Solution Diagram

✅ Final Answer: $64^{\circ}$

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