Class : Geometry
Topic : Using proportions involving corresponding line segments
Aim : How can we use proportions involving corresponding line segments?
Objectives :
1) Students will students will know that properties of polygons that are similar.
HW # 48 :
Date : Wednesday December 21 st , 2011
Given:
∆𝐴𝐵𝐶 𝑚 < 𝐶 = 90
̅̅̅̅ ⊥ 𝐶𝐴
Prove:
𝐴𝐷
=
𝐴𝐵
𝐷𝐸
𝐵𝐶
Note : Selection of definitions, theorems and postulates from this unit:
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1) A line that is parallel to one side of a triangle and intersects the other two sides in different points cuts off a triangle similar to the given triangle .
2) Two triangles are similar if two angles of one triangle are congruent to two corresponding angles of the other .
3) If a line divides two sides of a triangle proportionally, the line is parallel to the third side.
4) If a line is parallel to one side of a triangle and intersects the other two sides, the line divides those sides proportionally .
5) If a line segment joins the midpoints of two sides of a triangle, the segment is parallel to the third side and its length is onehalf the length of the third side .
6) In a proportion, the product of the means is equal to the product of the extremes .
7) If two polygons are similar, then their corresponding angles are congruent and their corresponding sides are in proportion .
Do Now :
Given: 𝐴𝐵 ̅̅̅̅
Prove:
𝐴𝐸
𝐶𝐸
=
𝐵𝐸
𝐷𝐸
Statements Reasons
PROCEDURE :
Write the Aim and Do Now
Get students working!
Take attendance
Give Back HW
Collect HW
Go over the Do Now
In the proof above, what reason could we use to prove 𝐶𝐸 𝑥 𝐵𝐸 = 𝐴𝐸 𝑥 𝐷𝐸

Assignment #1 :
Given: Parallelogram ABCD
Prove: 𝐷𝐸 𝑥 𝐵𝐸 = 𝐹𝐸 𝑥 𝐶𝐸
Statements Reasons
Assignment #2 :
Given: ∆𝐴𝐵𝐶 ~∆𝐷𝐸𝐹
Prove:
𝐴𝐷
𝐷𝐺
=
𝐴𝐵
𝐷𝐸
Statements
D
G
Reasons
Theorem : If two triangles are similar, the lengths of corresponding altitudes have the same ratio as the lengths of any two corresponding sides.
Corollary : In two similar triangles, the lengths of any two corresponding line segments have the same ratio as the lengths of any pair of corresponding sides.
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