In the figure given below- AC - AD- What is the relation between AB and AD -B- AB - ADC- Cannot be determinedD- AB - AD

The correct option is B AB gt;AD In Δ ABC and Δ ACD, ∠ 1=∠ 3+∠ 4 nbsp; nbsp;[Exterior angle property of a triangle] But ∠ 1=∠ 2 nbsp; (∵ AC=AD and an ...

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Standard IX

Mathematics

Side-Angle Inequality Theorems

In the figure...

Question

In the figure given below, AC = AD. What is the relation between AB and AD?

A B = A D

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A B < A D

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A B > A D

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Cannot be determined

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Solution

The correct option is C $A B > A D$

In $Δ A B C$ and $Δ A C D$ ,
$∠ 1 = ∠ 3 + ∠ 4$ [Exterior angle property of a triangle]
But $∠ 1 = ∠ 2$ ( $∵ A C = A D$ and angles opposite to equal sides are equal)
$\Rightarrow ∠ 2 = ∠ 3 + ∠ 4$
$\Rightarrow ∠ 2 > ∠ 3$
Hence, $A B > A D$ . [Side opposite to greater angle is larger as compared to smaller angle]

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In the figure given below, AC = AD. What is the relation between AB and AD?

The correct option is C AB>AD In ΔABC and ΔACD, ∠1=∠3+∠4 [Exterior angle property of a triangle] But ∠1=∠2 (∵AC=AD and angles opposite to equal sides are equal) ⇒∠2=∠3+∠4 ⇒∠2>∠3 Hence, AB>AD. [Side opposite to greater angle is larger as compared to smaller angle]