Triangle Proportionality Theorem

Front

What is the Triangle Proportionality Theorem?

Back

The Triangle Proportionality Theorem states that if a line is drawn parallel to one side of a triangle, it divides the other two sides proportionally.

Tags

CCSS.HSG.SRT.A.2

Front

Define similar triangles.

Back

Similar triangles are 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.HSG.SRT.A.2

Front

What does it mean for two triangles to be similar?

Back

Two triangles are similar if their corresponding angles are equal and the lengths of their corresponding sides are proportional.

Tags

CCSS.HSG.CO.B.6

CCSS.8.G.A.2

Front

If two triangles are similar, what can be said about their corresponding sides?

Back

The ratios of the lengths of their corresponding sides are equal.

Tags

CCSS.HSG.SRT.A.2

Front

What is the significance of parallel lines in the Triangle Proportionality Theorem?

Back

Parallel lines create proportional segments on the other two sides of the triangle, allowing for the application of the theorem.

Tags

CCSS.HSG.SRT.B.4

Front

How do you determine if two triangles are similar using angle-angle (AA) similarity?

Back

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

Tags

CCSS.HSG.SRT.A.2

Front

What is the relationship between the sides of similar triangles?

Back

The lengths of corresponding sides of similar triangles are proportional to each other.

Tags

CCSS.8.G.A.2

CCSS.HSG.CO.B.6

Front

If triangle ABC is similar to triangle DEF, and AB = 4, DE = 8, what is the ratio of their corresponding sides?

Back

The ratio of their corresponding sides is 1:2.

Tags

CCSS.HSG.SRT.A.2

Front

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

Back

If triangle ABC is similar to triangle DEF, then (AB/DE) = (BC/EF) = (AC/DF).

Tags

CCSS.HSG.SRT.A.2

Front

If two triangles have sides in the ratio 3:5, what can be said about their areas?

Back

The ratio of their areas will be the square of the ratio of their corresponding sides, so (3^2):(5^2) = 9:25.