Download Geometry Fall 2016 Lesson 051 _Proving a quadrilateral is a

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Lesson Plan #51
Class: Geometry
Date: Tuesday January 17th, 2017
Topic: Parallelograms
Aim: How do we prove that a quadrilateral is a parallelogram?
Objectives:
1) Students will know the different ways to prove a quadrilateral is a parallelogram.
2) Students will be able to prove that a quadrilateral is a parallelogram.
HW #51:
Do Now:
1) Write the definition of a parallelogram
2) Write the definition of a parallelogram as two separate conditionals.
3) What would be a way to prove that a quadrilateral is a parallelogram?
PROCEDURE:
Write the Aim and Do Now
Get students working!
Take attendance
Give Back HW
Collect HW
Go over the Do Now
Assignment #1: Complete the proof below
Given: Quadrilateral 𝐴𝐵𝐶𝐷 with ̅̅̅̅
𝐴𝐵 ≅ ̅̅̅̅
𝐶𝐷 and ̅̅̅̅
𝐴𝐷 ≅ ̅̅̅̅
𝐵𝐶
Prove: ABCD is a parallelogram
Plan: Draw ̅̅̅̅
𝐴𝐶 . Prove ∆𝐴𝐵𝐶 ≅ ∆𝐶𝐷𝐴 by 𝑠. 𝑠. 𝑠. ≅ 𝑠. 𝑠. 𝑠.
Then use congruent alternate angles to prove that the opposite
sides of ABCD are parallel
Statements
Reasons
1. Quadrilateral 𝐴𝐵𝐶𝐷
1. Given
̅̅̅̅
2. Draw 𝐴𝐶
2. A line segment may be drawn joining 2 points.
3. ̅̅̅̅
𝐴𝐵 ≅ ̅̅̅̅
𝐶𝐷𝑠. ≅ 𝑠.
3.
̅̅̅̅ ≅ ̅̅̅̅
4.𝐴𝐷
𝐵𝐶 𝑠. ≅ 𝑠.
4.
̅̅̅̅ ≅ 𝐴𝐶
̅̅̅̅ 𝑠. ≅ 𝑠.
5.𝐴𝐶
5.
6. ∆𝐴𝐵𝐶 ≅ ∆𝐶𝐷𝐴
6.
7. < 𝐴𝐶𝐵 ≅< 𝐶𝐴𝐷
7.
̅̅̅̅ ∥ 𝐵𝐶
̅̅̅̅
8. 𝐴𝐷
8.
9. < 𝐷𝐶𝐴 ≅< 𝐵𝐴𝐶
9.
10. ̅̅̅̅
𝐷𝐶 ∥ ̅̅̅̅
𝐴𝐵
10.
11.𝐴𝐵𝐶𝐷 is a parallelogram
11.
Assignment #2: Write the theorem that we have just proven above
Theorem:
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Summary of ways to prove a quadrilateral is a parallelogram:
To prove that a quadrilateral is a parallelogram, prove any one of the following statements is true:
1) Both pairs of opposite sides are parallel.
2) Both pairs of opposite sides are congruent.
3) One pair of opposite sides are both congruent and parallel.
4) The diagonals bisect each other.
5) Both pairs of opposite angles are congruent.
Assignment #1:
Complete the exercises below:
Assignment #2:
3
Assignment #3:
Assignment #3:
4
Assignment #4:
Assignment #5:
Assignment #6:
5
If enough time:
I.
II.