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State true or false.

The angles opposite to equal sides of a triangle are equal.

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True

False

answer is A.

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Detailed Solution

It is given that a triangle have equal sides.
Draw a triangle

P Q R

where

P S

is the bisector of

∠ P

as shown in the figure given below.
The sides

P Q = P R

.
We have to prove that,

∠ Q = ∠ R

Consider

Δ P Q S

and

Δ P S R

from the figure given.

P S = P S

is common in both the triangles.

P Q = P R

which is given.

∠ Q P S = ∠ P R S

as is the bisector of

∠ P

.
Apply the SAS congruence rule

Δ P Q S ≅ Δ P S R

.
By congruent parts of congruent triangles,

∠ Q = ∠ R

.
Hence the angles are equal.
Hence the statement is true.
Therefore option 1 is correct.

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