Similar Triangles

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 Angle-Angle (AA) criterion for triangle similarity?

Back

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

Front

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

Back

Set up a proportion using the heights and shadows of the objects. For example, if a tall object casts a shadow, you can find the height of a shorter object by using the ratio of their heights to their shadows.

Front

If a 10 ft tall tree casts a 5 ft shadow, how tall is a 2.5 ft shadow from a lawn ornament?

Back

2.5 ft (using the proportion: 10/5 = x/2.5).

Front

What is the Side-Side-Side (SSS) criterion for triangle similarity?

Back

If the corresponding sides of two triangles are in proportion, then the triangles are similar.

Front

What is the Side-Angle-Side (SAS) criterion for triangle similarity?

Back

If one angle of a triangle is equal to one angle of another triangle and the sides including those angles are in proportion, then the triangles are similar.

Front

How do you determine if two triangles are similar using their angles?

Back

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

Front

If triangle ABC has angles of 30°, 60°, and 90°, what can you say about triangle DEF with angles of 30°, 60°, and 90°?

Back

Triangle DEF is similar to triangle ABC because they have the same angles.

Front

What is the relationship between the lengths of corresponding sides in similar triangles?

Back

The lengths of corresponding sides are proportional.

Front

If triangle XYZ is similar to triangle ABC and the length of side XY is 4 cm and side AB is 8 cm, what is the ratio of their sides?

Back

The ratio of their sides is 1:2.