Triangle Proportionality Theorems

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

If AB / AC = BD / DC, what can be inferred about triangles ABC and BDC?

Back

Triangles ABC and BDC are similar by the Side-Splitter Theorem.

Tags

CCSS.HSG.SRT.A.2

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.

Tags

CCSS.HSG.SRT.A.2

Front

What is the SAS similarity criterion?

Back

SAS (Side-Angle-Side) similarity criterion states that if two sides of one triangle are proportional to two sides of another triangle and the included angles are equal, then the triangles are similar.

Tags

CCSS.HSG.SRT.B.5

Front

What is the SSS similarity criterion?

Back

SSS (Side-Side-Side) similarity criterion states that if the corresponding sides of two triangles are in proportion, then the triangles are similar.

Tags

CCSS.HSG.SRT.B.5

Front

If AB / BM = AC / ? and AB = 6, BM = 4, AC = 8, find the missing side.

Back

The missing side is 5 (AC = 6/4 * 5).

Tags

CCSS.HSG.SRT.B.4

Front

What is the significance of the proportional segments in a triangle?

Back

Proportional segments in a triangle help in determining the similarity of triangles and solving for unknown lengths.

Tags

CCSS.HSG.SRT.B.4

Front

How do you find the length of a segment using the Triangle Proportionality Theorem?

Back

To find the length of a segment, set up a proportion based on the lengths of the sides divided by the segments created by a parallel line.

Tags

CCSS.HSG.CO.C.9

Front

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

Back

The corresponding sides of similar triangles are in proportion.

Tags

CCSS.HSG.SRT.A.2

Front

What is the relationship between the angles of similar triangles?

Back

The corresponding angles of similar triangles are equal.

Tags

CCSS.HSG.SRT.A.2