[883]3.4A-Angles in Similar Triangles

Front

What is the Angle-Angle (AA) similarity criterion for triangles?

Back

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

Front

What does it mean for triangles to be similar?

Back

Triangles are similar if their corresponding angles are equal and their corresponding sides are in proportion.

Front

How can you determine if two triangles are similar using angle measures?

Back

If two triangles have two pairs of corresponding angles that are equal, they are similar.

Front

What is the relationship between the sides of similar triangles?

Back

The ratios of the lengths of corresponding sides of similar triangles are equal.

Front

If triangle A has angles of 30°, 60°, and 90°, what are the angles of a similar triangle?

Back

The angles of a similar triangle will also be 30°, 60°, and 90°.

Front

What is the significance of the third angle in triangle similarity?

Back

If two angles are known to be equal, the third angle must also be equal due to the triangle sum theorem.

Front

How do you find a missing side in similar triangles?

Back

Use the proportion of the lengths of corresponding sides to set up a ratio and solve for the missing side.

Front

If triangle A has sides of lengths 3, 4, and 5, and triangle B is similar to triangle A with a side of length 6, what is the length of the corresponding side in triangle A?

Back

The corresponding side in triangle A is 4. (Using the ratio 6/4 = 3/x)

Front

What is the Triangle Sum Theorem?

Back

The sum of the interior angles of a triangle is always 180°.

Front

Can two triangles be similar if only one pair of angles is equal?

Back

No, two triangles cannot be similar with only one pair of equal angles; at least two pairs must be equal.