similar shapes and missing sides

Front

What are similar shapes?

Back

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

Front

What is a scale factor?

Back

A scale factor is a number that scales, or multiplies, some quantity. In similar shapes, it is the ratio of the lengths of corresponding sides.

Front

If triangle ABC is similar to triangle XYZ, and the length of side AB is 10 and side XY is 25, what is the scale factor?

Back

The scale factor is 2.5 (25/10).

Front

How do you find a missing side in similar triangles?

Back

To find a missing side, set up a proportion using the lengths of the corresponding sides of the similar triangles.

Front

If the sides of triangle ABC are 4, 6, and 8, and triangle XYZ is similar with a scale factor of 3, what are the lengths of triangle XYZ?

Back

The lengths of triangle XYZ are 12, 18, and 24.

Front

What is the relationship between corresponding angles in similar shapes?

Back

Corresponding angles in similar shapes are equal.

Front

If two triangles are similar and one side of the first triangle is 5 and the corresponding side of the second triangle is 15, what is the scale factor?

Back

The scale factor is 3 (15/5).

Front

How can you determine if two shapes are similar?

Back

Two shapes are similar if their corresponding angles are equal and the lengths of their corresponding sides are proportional.

Front

If triangle DEF is similar to triangle GHI and the length of side DE is 9 and side GH is 27, what is the length of side EF if side HI is 18?

Back

The length of side EF is 6.

Front

What does it mean if two triangles are said to be 'in proportion'?

Back

It means that the ratios of the lengths of their corresponding sides are equal.