Proving Triangles are Similar

Front

What does it mean for two triangles to be similar?

Back

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

Front

What is the AA similarity postulate?

Back

The AA (Angle-Angle) similarity postulate states that if two angles of one triangle are equal to two angles of another triangle, then the triangles are similar.

Front

What is the SAS similarity theorem?

Back

The SAS (Side-Angle-Side) similarity theorem states that if two sides of one triangle are in proportion to two sides of another triangle and the included angles are equal, then the triangles are similar.

Front

What is the SSS similarity theorem?

Back

The SSS (Side-Side-Side) similarity theorem states that if the corresponding sides of two triangles are in proportion, then the triangles are similar.

Front

How can you determine if triangles are similar using the AA postulate?

Back

To determine if triangles are similar using the AA postulate, check if two angles of one triangle are equal to two angles of another triangle.

Front

How can you determine if triangles are similar using the SAS theorem?

Back

To determine if triangles are similar using the SAS theorem, check if two sides of one triangle are proportional to two sides of another triangle and the included angles are equal.

Front

How can you determine if triangles are similar using the SSS theorem?

Back

To determine if triangles are similar using the SSS theorem, check if the ratios of the lengths of corresponding sides of the triangles are equal.

Front

What is the relationship between similar triangles and their areas?

Back

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding side lengths.

Front

If triangle ABC is similar to triangle DEF, what can be said about their corresponding angles?

Back

If triangle ABC is similar to triangle DEF, then angle A = angle D, angle B = angle E, and angle C = angle F.

Front

If the sides of triangle ABC are 3, 4, and 5, and the sides of triangle DEF are 6, 8, and 10, are the triangles similar?

Back

Yes, triangle ABC and triangle DEF are similar because the sides are in proportion (3:6 = 1:2, 4:8 = 1:2, 5:10 = 1:2).