triangle proportionality Theorem

Front

What does it mean for two figures to be similar?

Back

Two figures are similar if they have the same shape but not necessarily the same size, meaning their corresponding angles are equal and their corresponding sides are proportional.

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

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

Back

The corresponding sides of similar triangles are proportional.

Front

What is the relationship between the angles of similar figures?

Back

The corresponding angles of similar figures are equal.

Front

What is a proportion in the context of geometry?

Back

A proportion is an equation that states that two ratios are equal.

Front

How do you find the missing value in a proportion?

Back

To find the missing value in a proportion, you can cross-multiply and solve for the unknown.

Front

What does the notation AB / BM = AC / CD represent?

Back

This notation represents a proportion where the ratio of segment AB to segment BM is equal to the ratio of segment AC to segment CD.

Front

What is the significance of parallel lines in triangles?

Back

Parallel lines in triangles create similar triangles and help establish proportional relationships between the sides.

Front

If DE is parallel to BC in triangle ABC, what can be inferred about the segments created?

Back

If DE is parallel to BC, then the segments created by the intersection of DE with AB and AC are proportional to the corresponding segments of triangle ABC.

Front

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

Back

The length of a side in similar triangles can be found using the formula: (length of side in triangle 1) / (length of corresponding side in triangle 2) = (scale factor).