Triangle Similarity Flashcard

Front

What is Triangle Similarity?

Back

Triangle similarity means that two triangles have the same shape but may differ in size. Their corresponding angles are equal, and their corresponding sides are in proportion.

Front

What are the criteria for triangle similarity?

Back

The three criteria for triangle similarity are: 1. AA (Angle-Angle) Criterion: If two angles of one triangle are equal to two angles of another triangle, the triangles are similar. 2. SSS (Side-Side-Side) Criterion: If the sides of one triangle are in proportion to the sides of another triangle, the triangles are similar. 3. SAS (Side-Angle-Side) Criterion: If two sides of one triangle are in proportion to two sides of another triangle and the included angle is equal, the triangles are similar.

Front

What does the AA criterion state?

Back

The AA criterion states that if two angles of one triangle are equal to two angles of another triangle, then the two triangles are similar.

Front

What does the SSS criterion state?

Back

The SSS criterion states that if the lengths of the corresponding sides of two triangles are in proportion, then the triangles are similar.

Front

What does the SAS criterion state?

Back

The SAS criterion states that if two sides of one triangle are in proportion to two sides of another triangle and the included angle is equal, then the triangles are similar.

Front

If triangle ABC is similar to triangle DEF, what can we say about their 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 by the SSS criterion because the sides are in proportion (3:6, 4:8, 5:10).

Front

Solve the proportion: 3/4 = x/12. What is x?

Back

x = 9.

Front

What is the ratio of the number of girls to the total number of students in a class with 12 girls and 16 boys?

Back

The ratio of girls to total students is 12/(12+16) = 12/28 = 3/7.

Front

If two triangles have a corresponding angle of 60 degrees and the other angles are 30 degrees and 90 degrees, are they similar?

Back

Yes, they are similar by the AA criterion.