geometry: chapter 8 8.6: proportions and similar triangles
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GEOMETRY: Chapter 88.6: Proportions and Similar Triangles
Theorem 8.4. Triangle Proportionality Theorem
If a line parallel to one side of a triangle intersects the other two sides, then it divides the two side proportionally.
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 397.
Theorem 8.5. Converse of the Triangle Proportionality Theorem
If a line divides two sides of a triangle proportionally, then it is parallel to the third side.
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 397.
Ex. 1:In the diagram, , =15, 20,
and 12. What is the length of ?
RS PN MS SN
RP MR
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 398.
Ex. 1:
Answer: 9
In the diagram, , =15, 20,
and 12. What is the length of ?
RS PN MS SN
RP MR
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 398.
Ex. 2:
A brace is added to a tree house as shown. Explain why the brace is not parallel to the floor.
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 389.
Ex. 2:
A brace is added to a tree house as shown. Explain why the brace is not parallel to the floor.
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 389.
Theorem 8.6:
If three parallel lines intersect two transversals, then they divide the transversals proportionally.
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 398.
Theorem 8.7:
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.
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 398.
Ex. 3. Using the information in the diagram, find the distance between First Street and Main Street.
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 399.
Ex. 3. Using the information in the diagram, find the distance between First Street and Main Street.
Answer: 510 m
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 399.
Ex.4
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 391.
In the diagram, . Use the
given side lengths to find the length of .
ABD CBD
DC
Ex.4
Answer: 22 6/7Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 391.
In the diagram, . Use the
given side lengths to find the length of .
ABD CBD
DC
8.6, p. 502, #3-14 all, 21-28 all
(20 questions)