Homework 3: Similar Triangles

Front

What does AA~ stand for in triangle similarity?

Back

AA~ stands for Angle-Angle similarity, which states that if two angles of one triangle are equal to two angles of another triangle, the triangles are similar.

Front

What does SSS~ stand for in triangle similarity?

Back

SSS~ stands for Side-Side-Side similarity, which states that if the corresponding sides of two triangles are in proportion, the triangles are similar.

Front

What does SAS~ stand for in triangle similarity?

Back

SAS~ stands for Side-Angle-Side similarity, which states that if two sides of one triangle are in proportion to two sides of another triangle and the included angles are equal, the triangles are similar.

Front

What is the criterion for determining if two triangles are not similar?

Back

Two triangles are not similar if none of the similarity criteria (AA~, SSS~, SAS~) are satisfied.

Front

If two triangles have two equal angles, what can be concluded about them?

Back

If two triangles have two equal angles, they are similar by the AA~ criterion.

Front

How do you find a missing side in similar triangles?

Back

To find a missing side in similar triangles, set up a proportion using the lengths of the corresponding sides.

Front

What is the similarity statement for triangles ΔMNL and ΔOPQ if they are similar?

Back

The similarity statement is ΔMNL ∼ ΔOPQ.

Front

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

Back

The corresponding angles of triangle ABC and triangle DEF are equal.

Front

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

Back

Yes, triangle GHI and triangle JKL are similar by SSS~ because their corresponding sides are in proportion (1:2).

Front

What is the relationship between the ratios of the areas of two similar triangles?

Back

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