Question 1

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

Accepted Answer

When the corresponding angles of two triangles are equal, the triangles are known as equiangular triangles. According to the AAA (Angle-Angle-Angle) similarity criterion, equiangular triangles are similar to each other. Therefore, the correct option is that the triangles are similar.

Question 2

All circles are:

Accepted Answer

All circles have the same shape regardless of their radii, although their sizes may vary. Geometric figures that have the same shape but not necessarily the same size are defined as similar figures. Hence, all circles are similar.

Question 3

All squares are:

Accepted Answer

Every square has four equal sides and each interior angle is 90 degrees. Therefore, all squares have the same shape but can have different side lengths. Figures with the same shape are similar.

Question 4

All equilateral triangles are:

Accepted Answer

In an equilateral triangle, all three sides are equal and each angle is 60 degrees. Since the angles are always equal regardless of the side length, all equilateral triangles are similar.

Question 5

If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio. This theorem is known as:

Accepted Answer

This fundamental theorem is known as Thales's Theorem or the Basic Proportionality Theorem (BPT). It states that if a line is parallel to a side of a triangle intersecting the other two sides, then it divides the two sides in the same ratio.

Triangles