mrs. mcconaughy geometry1 lesson 8.5 proportions and similar triangles objectives: to use...
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Mrs. McConaughy Geometry 1
LESSON 8.5 Proportions and Similar Triangles
OBJECTIVES: To use proportionality theorems to calculate segment lengthsTo solve real-life problems by using proportions in triangles
Mrs. McConaughy Geometry 2
THEOREM: TRIANGLE PROPORTIONALITY THEOREM If a line parallel to one side of a triangle, intersect the othertwo sides, then _________________________________________.
it divides the other two sides proportionally
PRT RU
TU QS, then = TQ US.
I f
Mrs. McConaughy Geometry 3
THEOREM: CONVERSE OF TRIANGLE PROPORTIONALITY THEOREM If a line divides two sides of a triangle proportionally, then___________________________________________________________
PRT RU
= , then TU QSTQ US.
I f
it is parallel to the third side.
Mrs. McConaughy Geometry 4
EXAMPLE: Finding the length of a segment
Use the TriangleProportionalityTheorem to find y.
CM = ___ MB ___ = ___
Mrs. McConaughy Geometry 5
EXAMPLE: Determining Parallel Lines
Given the diagram, determine whether MN || GH.
LM = ___ = ___
MGLN = ___ = ___
NH
MN ___________ GH
because________.
Mrs. McConaughy Geometry 6
THEOREM: COROLLARY TO TRIANGLE PROPORTIONALITY THEOREM If three parallel lines intersect two transversals, then __________________________________________. a = __
b
they divide the sides proportionally.
Mrs. McConaughy Geometry 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
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 ___ = ___
Mrs. McConaughy Geometry 10
FINAL CHECKS FOR UNDERSTANDING
1. In the diagram, 1 2 3. PQ = 9, QR = 15, and ST = 11. What is the length of ?
TU
Mrs. McConaughy Geometry 11
2. 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?
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