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Lesson Plan #48
Class: Geometry
Date: Wednesday December 18th, 2013
Topic: Proportions involving line segments
Aim: How do we solve proportions involving line segments?
Objectives:
1) Students will be able to solve proportions involving line segments in a triangle.
HW #48:
Pg. 272 #’s 3-11
Do Now
̅̅̅̅ .
2) In ∆𝐴𝐵𝐶, ̅̅̅̅
𝐷𝐸 ∥ 𝐵𝐶
Set up the ratio of 𝐴𝐷 𝑡𝑜 𝐷𝐵.
Set up the ratio of 𝐴𝐸 𝑡𝑜 𝐸𝐶.
What do you notice about those two ratios?
PROCEDURE:
Write the Aim and Do Now
Get students working!
Take attendance
Give Back HW
Collect HW
Go over the Do Now
Postulate: If a line is parallel to one side of a triangle and intersects the other two sides,
the line divides those sides proportionally.
Let’s list the proportions that can be set:
Example #1:
̅̅̅ intersecting 𝑅𝑆
̅̅̅̅ in 𝐾 and 𝑅𝑇
̅̅̅̅ in 𝐿. If 𝑅𝐾 = 5 𝑖𝑛., 𝐾𝑆 = 10𝑖𝑛., and 𝑅𝑇 = 18𝑖𝑛.,
In triangle RST, a line is drawn parallel to ̅𝑆𝑇
find 𝑅𝐿.
Postulate: If a line divides two sides of a triangle proportionally, the line is parallel to the third side
Example #2:
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Assignment #1:
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Assignment #2:
̅̅̅̅ is drawn ∥to 𝐵𝐶
̅̅̅̅ .
𝐺𝐻
What is the ratio of 𝐴𝐷 to 𝐷𝐺?
What is the ratio of 𝐴𝐸 to 𝐸𝐻?
G
H
What is the ratio of 𝐷𝐺 to 𝐺𝐵?
What is the ratio of 𝐸𝐻 to 𝐻𝐶?
What can we say if three parallel lines intersect two transversals?
Theorem: If three parallel lines intersect two transversals, then they divide the
transversals proportionally
Example:
Find the value of x in the figure at right.
Find the value of x in the figure at right
Online Activity:
http://www.mathwarehouse.com/geometry/similar/triangles/side-splitter-theorem.php
Online Activity:
http://www.geogebra.org/en/upload/files/english/nebsary/AngleBisectorTheorem/AngleBisectorFinal.html
Theorem:
If a ray bisects an angle of a triangle, then it divides the opposite side into segments proportional to the other side.
Online Activity:
http://www.mathwarehouse.com/geometry/similar/triangles/angle-bisector-theorem.php
Assignment #3:
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