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SAS Similarity

If ∆ABC and ∆...

Question

If $∆$ ABC and $∆$ PQR are congruent, then AB and ______________ are corresponding sides.

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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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ABC, sides AB and BC are congruent
(i) A-P-C, then show that BP < congruent sides.
(ii) If A-C-P, then show that BP > congruent sides.

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 ∆ABC and ∆PQR, ∠A = ∠Q, ∠B = ∠R and AB = QR, then these triangles are congruent by _______.

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

Q. If two congruent triangles

△ A B C and △ P Q R

are joined together so as to form a parallelogram, then which corresponding sides of the two triangles are joined together?

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