similar shapes and missing sides

Front

What are similar shapes?

Back

Shapes that have the same shape but different sizes. Their corresponding angles are equal, and their corresponding sides are in proportion.

Front

What is a scale factor?

Back

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

Front

If two triangles are similar, how do you find the length of a missing side?

Back

Use the scale factor between the triangles to set up a proportion and solve for the missing side.

Front

Triangle ABC is similar to triangle DEF. If the length of side AB is 6 cm and side DE is 9 cm, what is the scale factor?

Back

The scale factor is 9/6 or 3/2.

Front

If triangle ABC has sides of lengths 4 cm, 6 cm, and 8 cm, and triangle XYZ is similar to it with the shortest side measuring 6 cm, what is the length of the longest side in triangle XYZ?

Back

The longest side in triangle XYZ is 12 cm.

Front

What does it mean for two figures to be similar?

Back

It means they have the same shape but may differ in size, with corresponding angles equal and sides in proportion.

Front

If two similar triangles have a scale factor of 2:3, and the length of a side in the smaller triangle is 4 cm, what is the length of the corresponding side in the larger triangle?

Back

The length of the corresponding side in the larger triangle is 6 cm.

Front

How do you set up a proportion to find a missing side in similar triangles?

Back

Set the ratio of the lengths of the corresponding sides equal to each other and solve for the missing side.

Front

If triangle ABC is similar to triangle XYZ and the lengths of sides are in the ratio 1:4, what is the length of side X if side A is 5 cm?

Back

Side X is 20 cm.

Front

What is the relationship between the angles of similar shapes?

Back

The corresponding angles of similar shapes are equal.