1. LESSON 8.5 Proportions and Similar Triangles
OBJECTIVES:
To use proportionality theorems to calculate segment lengths
To solve real-life problems by using proportions in triangles
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2. Mrs. McConaughy Geometry
THEOREM: TRIANGLE PROPORTIONALITY THEOREM If a line parallel to one side of a triangle, intersect the other
two sides, then
_____________ ______________ ______________.
it divides the other two sides proportionally
Mrs. McConaughy Geometry

3. Mrs. McConaughy Geometry
THEOREM: CONVERSE OF TRIANGLE
PROPORTIONALITY THEOREM
If a line divides two sides of a triangle proportionally, then_________________ _____________________ _____________________
it is parallel to the third side.
Mrs. McConaughy Geometry

4. EXAMPLE: Finding the length of a segment
Use the Triangle
Proportionality
Theorem to find y.
CM = ___ MB
___ = ___
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5. EXAMPLE: Determining Parallel Lines
Given the diagram,
determine whether
MN || GH.
LM = ___ = ___ MG
LN = ___ = ___ NH
MN ___________ GH
because________.
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6. Mrs. McConaughy Geometry
THEOREM: COROLLARY TO TRIANGLE PROPORTIONALITY THEOREM
If three parallel lines intersect two transversals, then ______________ ______________ ______________.
they divide the sides proportionally.
a = __ b
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7. EXAMPLE: Using the corollary to the Triangle Proportionality Theorem
The segments joining the sides of trapezoid RSTU are parallel to its bases. Find x and y.
Mrs. McConaughy Geometry

8. Mrs. McConaughy Geometry
THEOREM: TRIANGLE-ANGLE- BISECTOR THEOREM
If a ray bisects an angle
of a triangle, then it
____________________ _____________________ _____________________ _____________________
_______.
divides the opposite side into segments whose lengths are proportional to the lengths of the other two sides.
a = __; a = __
b p
a = ___; a = ___
b p
Mrs. McConaughy Geometry

9. EXAMPLE: Using the Triangle-Angle-Bisector Theorem
Find the value of x.
IG = ___ GH
___ = ___
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10. FINAL CHECKS FOR UNDERSTANDING
1. In the diagram,
PQ = 9, QR = 15, and ST = 11. What is the length of ?
Mrs. McConaughy Geometry

11. Mrs. McConaughy Geometry
Find x.
3. The real estate term for distance along the edge of a piece of property that touches the ocean is “ocean frontage.” Find the ocean frontage for each lot shown.
Which of these lots should be listed for the highest price?
Mrs. McConaughy Geometry

12. Mrs. McConaughy Geometry
Homework Assignment:
Mrs. McConaughy Geometry