"Given: RS―⊥AB―,CB―⊥AC― Prove: △BSR∼△BCA" was answered by our experts

High School
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High school geometry
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Wotzdorfg

Answered question

2021-08-14

Given: $\overset{―}{R S} ⊥ \overset{―}{A B}, \overset{―}{C B} ⊥ \overset{―}{A C}$
Prove: $△ B S R \sim △ B C A$

Answer & Explanation

SoosteethicU

Skilled2021-08-15Added 102 answers

Now,
$\overset{―}{R S} ⊥ \overset{―}{A B} \Rightarrow m ∠ R S B = 90^{\circ}$
And
$\overset{―}{C B} ⊥ \overset{―}{A C} \Rightarrow m ∠ A C B = 90^{\circ}$
To prove: $△ B S R \sim △ B C A$
In $△ B S R and △ B C A$
$m ∠ R S B = m ∠ A C B = 90^{\circ}$
$m ∠ R B S = m ∠ A B C$ = common angle
$∴ △ B S R \sim △ B C A$ by Angle−Angle similarity theorem
(Angle−Angle similarity theorem:If two angles of one triangle are equal to two angles of another triangle,then the triangles are similar)
Hence, proved.

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