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Line l is the bisector of an angle A and B is any point on l.

Question

Line $l$ is the bisector of an angle $∠ A$ and $B$ is any point on $l$ . $BP$ and $BQ$ are perpendiculars from $B$ to the arms of $∠ A$ . Show that:
(i) $△ A BP ≅ △ A QB$
(ii) $BP = BQ$ or $B$ is equidistant from the arms of $∠ A$ .

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Line

l

is the bisector of an angle

∠ A

and

B

is any point on

l

BP

and

BQ

are perpendiculars from

B

to the arms of

∠ A

. Show that:
(i)

△ A BP ≅ △ A QB

(ii)

BP = BQ

B

is equidistant from the arms of

∠ A

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Text solutionVerified

△ A PB

and

△ A QB

∠ A PB = ∠ A QB

(Each

9 0^{o}

)

∠ P A B = ∠ Q A B

(

l

is the angle bisector of

∠ A

)

A B = A B

(Common)

∴ △ A PB ≅ △ A QB

(By AAS congruence rule)

∴ BP = BQ

(By CPCT)

It can be said that

B

is equidistant from the arms of

∠ A

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Question Text	Line $l$ is the bisector of an angle $∠ A$ and $B$ is any point on $l$ . $BP$ and $BQ$ are perpendiculars from $B$ to the arms of $∠ A$ . Show that: (i) $△ A BP ≅ △ A QB$ (ii) $BP = BQ$ or $B$ is equidistant from the arms of $∠ A$ .
Answer Type	Text solution:1
Upvotes	150

Line l is the bisector of an angle ∠A and B is any point on l. BP and BQ are perpendiculars from B to the arms of ∠A. Show that:(i) △ABP≅△AQB(ii) BP=BQ or B is equidistant from the arms of ∠A.

Text solutionVerified

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Line $l$ is the bisector of an angle $∠ A$ and $B$ is any point on $l$ . $BP$ and $BQ$ are perpendiculars from $B$ to the arms of $∠ A$ . Show that:
(i) $△ A BP ≅ △ A QB$
(ii) $BP = BQ$ or $B$ is equidistant from the arms of $∠ A$ .