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ASA Criteria for Congruency

If perpendicu...

Question

If perpendiculars from any point within an angle on its arms are congruent, prove that it lies on the bisector of that angle.

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Solution

Let P be a point within such that

We have to prove that P lies on the bisector of

In and we have

(We have)

(Common)

So by right hand side congruence criterion, we have

So,

Hence P lies on the bisector of proved.

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Similar questions

Q. In the given figure, line

l

is the bisector of an angle

A

B

is any point on

l .

B P

B Q

are perpendiculars from

B

∠ A .

B

is equidistant from the arms of

∠ A .

Q. In the given figure, line l is the bisector of an angle ∠A and B is any point on l. If BP and BQ are perpendiculars from B to the arms of ∠A, show that
(i) ΔAPB ≅ ΔAQB
(ii) BP = BQ, i.e., B is equidistant from the arms of ∠A.

Q. Line l is the bisector of an angle

∠ A a n d B

is any point on l. BP and BQ are perpendiculars from B to the arms of

∠ A

(see the given figure). Show that:

Δ A P B ≅ Δ A Q B

Q. Question 5 (ii)
Line l is the bisector of an angle

∠ A a n d B

is any point on l. BP and BQ are perpendiculars from B to the arms of

∠ A

(see the given figure). Show that:
BP = BQ or B is equidistant from the arms of

∠ A .

l

is the bisector of an angle

∠ A

B

is any point on

l

B P

B Q

are perpendiculars from

B

∠ A

. Show that:
(i)

△ A B P ≅ △ A Q B

B P = B Q

B

is equidistant from the arms of

∠ A

.

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