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Relation between Areas and Sides of Similar Triangles

Two triangles...

Question

Two triangles are similar by SAS similarity if,

A

Two sides are equal and angles contained by the sides are equal.

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B

The ratio of two corresponding sides is equal and the angles contained by the sides are equal.

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C

The ratio of two corresponding sides is equal and all the angles are equal.

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D

The ratio of two corresponding sides is equal and all the corresponding angles are equal.

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Solution

The correct option is B The ratio of two corresponding sides is equal and the angles contained by the sides are equal.
SAS similarity states that two triangles are similar if ratio of two corresponding sides is equal and the included angles are equal.

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Similar questions

Q. Two triangles are similar by SAS similarity if, the ratio of two corresponding sides is equal and the included angles are equal.

Q. Statement 1: In two triangles, if two corresponding angles are equal, it’s not required to check whether the ratio of their corresponding sides is equal or not to state whether they are similar.
Statement 2: When two triangles are similar, the ratio of their corresponding sides is equal.

Q. If in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio and hence the two triangles are similar.

Q. Fill in the blanks using the correct word given in brackets :

(i) All circles are ......... (congruent, similar).
(ii) All squares are ........(similar, congruent).
(iii) All .......... triangles are similar (isosceles, equilateral):
(iv) Two triangles are similar, if their corresponding angles are .......... (proportional, equal)
(v) Two triangles are similar, if their corresponding sides are ........... (proportional, equal)
(vi) Two polygons of the same number of sides are similar, if (a) their corresponding angles are and (b) their corresponding sides are ...........(equal, proportional).

Q. Prove that if in two triangles, corresponding angles are equal then their corresponding sides are in the same ratio and hence the two triangles are similar.

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