Over Lesson 7–4
If AB = 4, BC = 7, ED = 5, and EC = 13.75, determinewhether BD || AE.
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In the diagram, 1st Street is parallel to 3rd Street and 5th Street. Find the distance from 3rd Street to 5th Street if you are traveling on 4th Street.
Content Standards
G.SRT.4 Prove theorems about triangles.
G.SRT.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
Mathematical Practices
1 Make sense of problems and persevere in solving them.
3 Construct viable arguments and critique the reasoning of others.
7.5: Parts of Similar Triangles
I will be able to…
•Recognize and use proportional relationships of corresponding angle bisectors, altitudes, and medians of similar triangles.
• Solve for missing parts using the Triangle Bisector Theorem.
• What is a median?Segment drawn from a vertex to the midpoint of the
opposite side
• What is an altitude?Segment drawn from a vertex that is perpendicular to the
opposite side
• What is an angle bisector?Segment that bisects an angle and is drawn to the opposite
side
Recall…
Key Question:
Based on what we’ve learned the past few days,
how do you think the altitudes, medians, and angle bisectors are related between similar triangles?
Similar Triangle Proportionality
• If two triangles are similar, then the ratio of any two corresponding lengths (including altitudes, medians and angle bisector segments) is equal to the scale factor of the similar triangles (aka proportional!)
Use Special Segments in Similar Triangles
In the figure, ΔLJK ~ ΔSQR. Find the value of x.
Answer: x = 7.5
Use the Triangle Angle Bisector Theorem
Find x.
Since the segment is an angle bisector of the triangle, the Angle Bisector Theorem can be used to write a proportion.
Answer: x = 10