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.

Tags

CCSS.8.G.A.2

CCSS.HSG.CO.B.6

Front

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

Back

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

Tags

CCSS.HSG.SRT.A.2

Front

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

Back

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

Tags

CCSS.HSG.SRT.B.5

Front

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

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.

Tags

CCSS.HSG.SRT.B.5

Front

How do you set up a proportion for similar triangles?

Back

By comparing the lengths of corresponding sides of the triangles, you can create a ratio that can be solved for unknown lengths.

Tags

CCSS.HSG.SRT.A.2

Front

If triangle ABC is similar to triangle DEF, and AB = 4, AC = 6, and DE = 8, what is the length of DF?

Back

DF = 6 (using the proportion: AB/DE = AC/DF => 4/8 = 6/DF => DF = 6).

Tags

CCSS.HSG.SRT.A.2

Front

What is the formula for finding the length of a side in similar triangles?

Back

If triangles are similar, then \( \frac{a}{b} = \frac{c}{d} \), where a and b are corresponding sides, and c and d are the sides of the other triangle.

Tags

CCSS.HSG.SRT.A.2

Front

Solve for h in the proportion \( \frac{10}{h} = \frac{2}{10} \).

Back

h = 50.

Tags

CCSS.7.G.A.1

Front

If two triangles have sides in the ratio 3:5, and the shorter side of the first triangle is 9, what is the length of the shorter side of the second triangle?

Back

The shorter side of the second triangle is 15 (using the ratio: 9/x = 3/5 => x = 15).

Tags

CCSS.7.G.A.1

Front

What is the relationship between the areas of similar triangles?

Back

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