Question

ABC is a right triangle right angled at A and AD is perpendicular to BC show that BD/AD =AB/AC

Answer 1

Answer:

proved in above picture

Answer 2

Answer:

The ratio of proportional sides BD/AD = AB/AC are equal.

Step-by-step explanation:

Given: In ΔABC, ∠A = 90° and AD is perpendicular to BC, i.e., AD ⊥ BC.

To prove: BD/AD = AB/AC

From the figure,

∠CAD + ∠BAD = 90° . . . . . (1)

Also, ∠BAD + ∠ABD = 90° . . . . . (2) (Since ∠ADB = 90°)

From (1) and (2), we have

∠CAD = ∠ABD . . . . . (3)

Consider the ΔADB and ΔADC,

∠ADB = ∠ADC (Each 90°)

∠ABD = ∠CAD (From 3)

By angle similarity test, ΔADB ≈ ΔADC

⇒ BD/AD = AB/AC (Corresponding sides are proportional)

Hence proved.

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