Honors Geometry - Triangle Proportionality Theorem

Front

What is the Triangle Proportionality Theorem?

Back

If a line is drawn parallel to one side of a triangle, it divides the other two sides proportionally.

Front

State the formula for the Triangle Proportionality Theorem.

Back

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

How do you set up a proportion using the Triangle Proportionality Theorem?

Back

Identify the segments created by the parallel line and set up the proportion using the lengths of the segments.

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Back

Cross-multiply to get: 6x = 21 * 7, then solve for x.

Front

What is the significance of parallel lines in triangles?

Back

Parallel lines create proportional segments on the triangle's sides, allowing for the application of the Triangle Proportionality Theorem.

Front

What is a proportion?

Back

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

Front

How can you prove that two segments are proportional?

Back

By showing that the ratios of the lengths of the segments are equal.

Front

What is the relationship between similar triangles and the Triangle Proportionality Theorem?

Back

The Triangle Proportionality Theorem is used to establish the similarity of triangles by proving that corresponding sides are proportional.

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Back

It can be inferred that the segments KL and HJ are proportional to segments KG and LG.