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.

Front

State the similarity postulate that can be used to prove triangles are similar when two angles are equal.

Back

AA (Angle-Angle) Similarity Postulate: If two angles of one triangle are equal to two angles of another triangle, then the triangles are similar.

Front

What does it mean for two triangles to be similar?

Back

Two triangles are similar if their corresponding angles are equal and their corresponding sides are in proportion.

Front

Back

The segments are proportional, which suggests that the triangles formed by these segments may be similar.

Front

What is the significance of parallel lines in relation to triangle similarity?

Back

Parallel lines create proportional segments in triangles, allowing the use of the Triangle Proportionality Theorem to establish similarity.

Front

How can you determine if two triangles are similar using the SAS similarity criterion?

Back

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 (SAS Similarity Criterion).

Front

What is the relationship between congruent triangles and similar triangles?

Back

All congruent triangles are similar, but not all similar triangles are congruent. Similar triangles have the same shape but may differ in size.

Front

Provide an example of a proportion that demonstrates the Triangle Proportionality Theorem.

Back

Front

What is the definition of similar figures?

Back

Similar figures are shapes that have the same shape but may differ in size, with corresponding angles equal and corresponding sides in proportion.

Front

What is the AA similarity criterion?

Back

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