Lesson 8.4 Proportionality Theorems Learning

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Lesson 8.4 Proportionality Theorems Learning

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Lesson 8.4 Proportionality Theorems Learning Target: Understand and use proportionality theorems. Success Criteria: I can use proportionality theorems to find lengths in triangles. I can find lengths when two transversals intersect three

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Lesson 8.4 Proportionality Theorems

Learning Target:
Understand and use proportionality theorems. Success Criteria:
I can use proportionality theorems to find lengths in triangles.
I can find lengths when two transversals intersect three parallel lines.
I can find lengths when a ray bisects an angle of a triangle.

Using the Triangle Proportionality Theorem

Example 1 Finding the Length of a Segment Triangle Proportionality Theorem Substitute. Multiply each side by 9. SOLUTION Find the length of RQ.

Example 2 Modeling Real Life Find and simplify the ratios of the lengths. SOLUTION

Recall that you partitioned a directed line segment in the coordinate plane in Section 3.5. You can apply the Triangle Proportionality Theorem to construct a point along a directed line segment that partitions the segment in a given ratio.

Construction Constructing a Point along a Directed Line Segment SOLUTION Step 1 Step 2 Step 3

Using Other Proportionality Theorems

Example 3 Using the Three Parallel Lines Theorem Find the distance HF between Main Street and South Main Street. Method 1 Use the Three Parallel Lines Theorem to write a proportion. Three Parallel Lines Theorem Substitute. Multiply each side by 120. So, the distance between Main Street and South Main Street is 360 yards. SOLUTION

Example 3 Using the Three Parallel Lines Theorem Method 2 Write a proportion involving total and partial distances. Step 1 Make a table to compare the distances. Step 2 Write and solve a proportion. Write proportion. Multiply each side by 120. So, the distance between Main Street and South Main Street is 360 yards.

Example 4 Using the Triangle Angle Bisector Theorem Triangle Angle Bisector Theorem Substitute. Cross Products Property Solve for x. SOLUTION

Lesson 8.4 Proportionality Theorems Learning

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