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Congruence of Triangles

If triangle A...

Question

If triangle ABC is congruent to triangle PQR, then

A

side AB is congruent to side QR

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B

angle P is congruent to angle B

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C

side PQ is congruent to side BC

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D

angle B is congruent to angle Q

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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 triangle ABC, line segment AB is congruent to line segment BC is congruent to line segment CA. Prove that angle A is congruent to angle B is congruent to angle C.

△ A B C

△ P Q R

∠ A = ∠ Q

∠ B = ∠ R .

Δ

P Q R

should be equal to side

A B

Δ A B C

so that the two triangles are congruent?

Q. If two sides of a right angled triangle is congruent to the corresponding sides of another right angle triangle then both the Triangles are congruent : true or false

△

ABC is congruent to

△

DEF as side AB = side DE and side BC = side EF, then,

∠

C corresponds to which angle of

△

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