Question

State true or false
1. All triangles are similar.
2. All squares are similar.
3. Circles with equal radius are always congruent.
4. Isosceles triangles are similar.
5. Equilateral triangles are similar.​

Answer 1

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1. False, All triangles are not similar. Their angles can vary.
2. True, All squares are similar as angles of square are always same i.e. 90°
3. True, Circles with equal radius are congruent.
4. False, Angle can vary.
5. True, As angles are always same i.e. of 60°

Answer 2

All triangles are similar is False as there are many shapes in triangles

All squares are similar is True

Circles with equal radius are always congruent is True

Isosceles triangles are similar is False

True, : All equilateral triangles are similar triangles as corresponding angles are congruent and corresponding sides are in proportion.

Providing detailed explanation for one case:

Equilateral Triangle

A triangle in which all the sides are of equal length is called an equilateral triangle.

Each of  the angles of an  equilateral triangle measures 60°

Equilateral triangle also called equiangular.

Similar Triangles

Two triangles are similar if their corresponding angles are congruent, and the corresponding sides are in proportion.

All the Equilateral triangles have Measures of each angle as 60° Hence Corresponding angles of two equilateral triangles are congruent

Hence using Angle-Angle-Angle Similarity Equilateral triangles are similar

Also even considering side length

Let say there are two equilateral  triangle one with side length m and other with n

Taking ratio of corresponding side = m/n for each Hence same

So triangles are similar as per SSS similarity also

Hence, Given statement is True that  All equilateral triangles are similar triangles