Geo - 6.2 Triangle Proportionality Theorem

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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.

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CCSS.HSG.SRT.A.2

Front

How can you determine if two lines are parallel in a triangle?

Back

Two lines are parallel if they divide the other two sides of the triangle proportionally.

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CCSS.HSG.SRT.B.4

Front

What does it mean for segments to be proportional?

Back

Segments are proportional if the ratios of their lengths are equal.

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CCSS.8.G.A.2

CCSS.HSG.CO.B.6

Front

If JL is parallel to MN, what can be inferred about the segments JK and KL?

Back

If JL is parallel to MN, then JK/KL = JM/MN.

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CCSS.HSG.SRT.B.4

Front

How do you solve for a missing segment length using the Triangle Proportionality Theorem?

Back

Set up a proportion based on the lengths of the segments and solve for the unknown.

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CCSS.HSG.CO.C.9

Front

What is the formula for finding the length of a segment when given proportional segments?

Back

If a/b = c/d, then ad = bc, which can be rearranged to find the unknown segment.

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CCSS.HSG.SRT.B.4

Front

What is the significance of the Triangle Proportionality Theorem in geometry?

Back

It helps in solving problems related to similar triangles and finding unknown lengths.

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CCSS.HSG.SRT.B.4

Front

How can you apply the Triangle Proportionality Theorem to real-world problems?

Back

By using the theorem to find distances or heights in similar triangles in various applications.

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CCSS.HSG.SRT.B.4

Front

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

Back

Similar triangles have corresponding sides that are proportional, which is a direct application of the Triangle Proportionality Theorem.

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CCSS.HSG.SRT.B.4

Front

What is the first step in solving a problem using the Triangle Proportionality Theorem?

Back

Identify the parallel lines and the segments they create.

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CCSS.HSG.SRT.B.4