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If Two Angles of a Triangle Are Congruent Then the Sides Opposite to Them Are Congruent

In the figure...

Question

In the figure below, the sides AB and AC are congruent, then the angles at B and C are _______ .

A

Never equal

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B

Always equal

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C

30 and 40 degrees always

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D

None of the above

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Solution

The correct option is B Always equal
According to isosceles triangle theorem, "If two sides of a triangle are congruent then the angles opposite to them are congruent"

So, the angles at B and C are always equal.

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In the given figure AD is the bisector of $∠$ A and AB = AC. Then, by which criterion $△$ ACD and $△$ ABD are congruent?

Q. Which of the following statements are true and which of them are false?

(i) All squares are congruent.
(ii) If two squares have equal areas, they are congruent.
(iii) If two figures have equal areas, they are congruent.
(iv) If two triangles are equal in area, they are congruent.
(v) If two sides and one angle of a triangle are equal to the corresponding two sides and angle of another triangle, the triangle are congruent.
(vi) If two angles and any side of a triangle are equal to the corresponding angles and the side of another triangle then the triangles are congruent.
(vii) If three angles of a triangle are equal to the corresponding angles of another triangle then the triangles are congruent.
(viii) If the hypotenuse and an acute angle of a right triangle are equal to the hypotenuse and the corresponding acute angle of another right triangle then the triangle are congruent.
(ix) If the hypotenuse of a right triangle is equal to the hypotenuse of another right triangle then the triangles are congruent.
(x) If two triangles are congruent then their corresponding sides and their corresponding angles are congruent.

Q. In the given figure, AD is bisector of

∠

=

Δ

Δ

ABD are congruent by which criterion?

Draw a labelled figure showing information in each of the following statements and write the antecedent and the consequent.

(i) Two equilateral triangles are similar.

(ii) If angles in a linear pair are congruent then each of them is a right angle.

(iii) If the altitudes drawn on two sides of a triangle are congruent then those two sides are congruent.

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If Two Angles of a Triangle Are Congruent Then the Sides Opposite to Them Are Congruent

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