Which of the following statements are true (T) and which are false(F) :
Angles opposite to equal sides of a triangle are equal.

True

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False

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Solution

The correct option is A True

In $△ A B C,$
$A B = A C$ [ Given ]
Draw a bisector $∠ A$ intersecting $B C$ at $D .$
In $△ B A D$ and $△ C A D$
$A B = A C$ [ Given ]
$∠ B A D = ∠ C A D$ [ By construction ]
$A D = A D$ [ Common side ]
$△ B A D ≅ △ C A D$ [ By $S A S$ congruence rule ]
$∴$ $∠ A B D = ∠ A C D$ [ By CPCT ]
$\Rightarrow$ $∠ B = ∠ C$
Hence, angles opposite to equal sides are equal.
$∴$ Given statement is true.

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Similar questions

Which of the following statements are true (T) and which are false (F):

(i) Sides opposite to equal angles of a triangle may be unequal.

(ii) Angles opposite to equal sides of a triangle are equal.

(iii) The measure of each angle of an equilateral triangle is 60°.

(iv) If the altitude from one vertex of a triangle bisects the opposite side, then the triangle may be isosceles.

(v) The bisectors of two equal angles of a triangle are equal.

(vi) If the bisector of the vertical angle of a triangle bisects the base, then the triangle may be isosceles.

(vii) The two altitudes corresponding to two equal sides of a triangle need not be equal.

(viii) If any two sides of a right triangle are respectively equal to two sides of other right triangle, then the two triangles are congruent.

(ix) Two right triangles are congruent if hypotenuse and a side of one triangle are respectively equal equal to the hypotenuse and a side of the other triangle.

Q. Let us define a statement as a sentence that can be judged to be true or false.
Which of the following is not a statement?
(a) 3 + 5 = 7.
(b) Kunal is a tall boy.
(c) The sum of the angles of a triangle is 90°.
(d) The angles opposite to equal sides of a triangle are equal.

Angles opposite the equal sides of a triangle are equal. True or False

Angles opposite to the equal sides of a triangle are equal.If true enter 1 else 0.

Q. Sides opposite to the equal angles of a triangle are not equal.

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Which of the following statements are true (T) and which are false(F) :Angles opposite to equal sides of a triangle are equal.

Which of the following statements are true (T) and which are false(F) :
Angles opposite to equal sides of a triangle are equal.