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SSS Criteria for Congruency

If ∆ABC and ∆...

Question

If $∆$ ABC and $∆$ PQR are congruent, then ____________ and vertex R are corresponding vertices.

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Solution

Congruent means that one figure is identical to another in shape and size.
In congruent triangles :
One triangle is identical to another in shape and size.
All the sides and angles of a triangle are equal to the corresponding sides and angles of its congruent triangle.

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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.

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seg RP. State two different one-one correspondences between the vertices of the triangles which are congruent.

If $∆$ ABC and $∆$ PQR are congruent, then vertex A and ______________ are corresponding vertices.

A B C D

P Q R S

are congruent. then

a =

.

In two triangles; if a pair of corresponding angles and a ___ are equal, then the triangles are necessarily congruent.

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