G-6.2 FLASHCARD Ratios Proportions and Similarity

Front

What is a ratio?

Back

A ratio is a comparison of two quantities by division, expressed as a fraction, decimal, or with a colon (e.g., 3:2).

Front

What does it mean for two ratios to be proportional?

Back

Two ratios are proportional if they express the same relationship, meaning their cross products are equal (e.g., a/b = c/d implies a*d = b*c).

Front

What are similar triangles?

Back

Similar triangles are triangles that have the same shape but may differ in size. Their corresponding angles are equal, and the ratios of their corresponding sides are proportional.

Front

How can you determine if two triangles are similar?

Back

Two triangles can be determined to be similar if: 1) Their corresponding angles are equal, or 2) The ratios of their corresponding sides are equal.

Front

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

Back

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

Front

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

Back

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

Front

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

Back

The SAS similarity criterion states that 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

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 ratios of their corresponding sides (3:6, 4:8, 5:10) are equal.

Front

What is a proportion?

Back

A proportion is an equation that states that two ratios are equal.