Similar Triangles & Proportions

Front

What are similar triangles?

Back

Triangles that have the same shape but may differ in size. Their corresponding angles are equal, and their corresponding sides are in proportion.

Front

What is the principle of proportionality in similar triangles?

Back

If two triangles are similar, the ratios of the lengths of their corresponding sides are equal.

Front

How can you find the height of an object using similar triangles?

Back

By creating a proportion between the height of the object and the distance from the object, compared to the height of a smaller object and its distance.

Front

What is a pair of corresponding sides in similar triangles?

Back

Sides that are in the same relative position in two different triangles.

Front

If triangle ABC is similar to triangle DEF, what can be said about angle A and angle D?

Back

Angle A is equal to angle D.

Front

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

Back

By equating the ratios of the lengths of corresponding sides.

Front

What is the formula for finding the area of similar triangles?

Back

If the ratio of the sides of two similar triangles is a:b, then the ratio of their areas is a²:b².

Front

If two triangles have sides in the ratio 3:4, what is the ratio of their areas?

Back

The ratio of their areas is 3²:4², which is 9:16.

Front

What is the significance of the AA (Angle-Angle) similarity criterion?

Back

If two angles of one triangle are equal to two angles of another triangle, the triangles are similar.

Front

How do you find the length of a side in a triangle using the properties of similar triangles?

Back

By using the known lengths of corresponding sides and setting up a proportion.