6.2.2 Missing Values in Similar Triangles

Front

What are similar triangles?

Back

Triangles that have the same shape but may differ in size. Their corresponding angles are equal, and their corresponding sides are in proportion.

Front

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

Back

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

Front

How do you find missing side lengths in similar triangles?

Back

Use the proportion of corresponding sides. If triangle A has sides a, b, c and triangle B has sides x, y, z, then \( \frac{a}{x} = \frac{b}{y} = \frac{c}{z} \).

Front

If triangle ABC is similar to triangle DEF, and the lengths of sides AB and DE are 6 and 9 respectively, what is the ratio of their sides?

Back

The ratio of their sides is \( \frac{6}{9} = \frac{2}{3} \).

Front

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

Back

If the corresponding sides of two triangles are in proportion, then the triangles are similar.

Front

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

Back

If one angle of a triangle is equal to one angle of another triangle and the sides including these angles are in proportion, then the triangles are similar.

Front

How do you determine if two triangles are similar?

Back

Check if they satisfy any of the similarity criteria: AA, SSS, or SAS.

Front

If two triangles have sides of lengths 4, 6, and 8, and 2, 3, and 4, are they similar?

Back

Yes, they are similar because the sides are in proportion (\( \frac{4}{2} = \frac{6}{3} = \frac{8}{4} = 2 \)).

Front

What is the relationship between the angles of similar triangles?

Back

The corresponding angles of similar triangles are equal.

Front

If triangle XYZ is similar to triangle PQR, and angle X = 50°, what is angle P?

Back

Angle P is also 50° because corresponding angles in similar triangles are equal.