Download Geometry Fall 2012 Lesson 050 _Using Similar triangles to prove

1
Lesson Plan #50
Date: Monday January 7th, 2013
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# 50:
Do Now:
Given:
∆𝐴𝐵𝐶
̅̅̅̅
𝐷𝐸 𝑖𝑠 𝑎 𝑚𝑖𝑑𝑠𝑒𝑔𝑚𝑒𝑛𝑡
Prove:
𝐴𝐵 𝐷𝐸
=
𝐴𝐶 𝐷𝐶
Statements
Reasons
1. ∆𝐴𝐵𝐶
1.
2. ̅̅̅̅
𝐷𝐸
2.
𝑖𝑠 𝑎 𝑚𝑖𝑑𝑠𝑒𝑔𝑚𝑒𝑛𝑡
3.
3.
Note: Selection of definitions, theorems and postulates from this unit:
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.
Assignment #1:
Given: ̅̅̅̅
𝐴𝐵 ∥ ̅̅̅̅
𝐷𝐶
Prove:
𝐴𝐸
𝐶𝐸
𝐵𝐸
= 𝐷𝐸
Statements
Reasons
2
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 #2:
̅̅̅̅̅̅ , Parallelogram ABCD
Given: 𝐷𝐸𝐹
Prove: 𝐷𝐸 𝑥 𝐵𝐸 = 𝐹𝐸 𝑥 𝐶𝐸
Statements
Assignment #3:
̅̅̅̅ and ̅̅̅̅
Given: ∆𝐴𝐵𝐶 ~∆𝐷𝐸𝐹, 𝐴𝐷
𝐷𝐺 are altitudes
𝐴𝐷
𝐴𝐵
Prove:
=
𝐷𝐺
𝐷𝐸
Reasons
D
G
Statements
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.
Assignment #4:
3
Assignment #5: Answer the following multiple choice questions:
A)
B)
Assignment #6: Complete the proof below:
Statements
Assignment #7:
Reasons