Similar Figures

Front

What are similar figures?

Back

Similar figures are shapes that have the same shape but may differ in size. Their corresponding angles are equal, and the ratios of their corresponding sides are proportional.

Front

What is the criteria for two triangles to be similar?

Back

Two triangles are similar if their corresponding angles are equal and the lengths of their corresponding sides are in proportion.

Front

If triangle ABC is similar to triangle DEF, and the lengths of sides AB and DE are 4 cm and 8 cm respectively, what is the ratio of their corresponding sides?

Back

The ratio of their corresponding sides is 1:2.

Front

What is the relationship between the lengths of shadows of similar figures?

Back

The lengths of the shadows of similar figures are proportional to their heights.

Front

If a tree's shadow is 32 feet long and Lance the alien's shadow is 8 feet long, what is the ratio of the tree's height to Lance's height if Lance is 5 feet tall?

Back

The ratio of the tree's height to Lance's height is 4:1.

Front

What does it mean if two parallelograms are similar?

Back

If two parallelograms are similar, it means their corresponding angles are equal and the ratios of their corresponding sides are proportional.

Front

How can you determine if two figures are similar?

Back

To determine if two figures are similar, check if their corresponding angles are equal and if the ratios of their corresponding sides are equal.

Front

If the lengths of two similar figures are in the ratio 3:5, what is the ratio of their areas?

Back

The ratio of their areas is 3²:5², which simplifies to 9:25.

Front

What is the value of x if triangle ABC is similar to triangle FGH and the sides are in the ratio 2:3?

Back

If the sides are in the ratio 2:3, then x can be found using the proportion based on the lengths of the sides.

Front

What is the significance of corresponding angles in similar figures?

Back

Corresponding angles in similar figures are equal, which is a key criterion for determining similarity.