Question

Fill in the blank
All …………………… triangles are similar.
A. Equilateral
B. Scalene
C. Isosceles
D. None of these

Answer 1

Hint:When two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion. Similar triangles are triangles that have the same shape, but their sizes may vary.

Complete answer:
Similar triangles are triangles that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion. We denote the similarity of triangles here by ‘~’ symbol.

Triangle is a three-sided polygon. The condition for the similarity of triangles is:
-Corresponding angles of both the triangles are equal, and
-Corresponding sides of both the triangles are in proportion to each other.

Properties of similar triangles:
-Both have the same shape but sizes may be different.
-Each pair of corresponding angles are equal.
-The ratio of corresponding sides is the same.

For equilateral triangles, each side is equal. Hence the ratio between two sides of different triangles will be constant. Hence all equilateral triangles are similar.Therefore the correct answer is equilateral triangles are similar.

Hence option A is the correct answer.

Note:Similar triangles are triangles that have the same shape, but their sizes may vary. When two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion. Do not confuse between similar triangles and congruent triangles which are the same in shape and size.