Download Geometry Fall 2011 Lesson 38 _Proving a quadrilateral is a

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esson Plan #38
Class: Geometry
Date: Monday November 28th, 2011
Topic: Parallelograms
Aim: What are some properties of parallelograms?
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 #38:
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 corresponding angles to prove that the
opposite sides of ABCD are parallel
Statements
1. Quadrilateral 𝐴𝐵𝐶𝐷
2. Draw ̅̅̅̅
𝐴𝐶
3. ̅̅̅̅
𝐴𝐵 ≅ ̅̅̅̅
𝐶𝐷
𝑠. ≅ 𝑠.
̅̅̅̅ ≅ 𝐵𝐶
̅̅̅̅
4. 𝐴𝐷
𝑠. ≅ 𝑠.
̅̅̅̅ ≅ 𝐴𝐶
̅̅̅̅
5. 𝐴𝐶
𝑠. ≅ 𝑠.
6. ∆𝐴𝐵𝐶 ≅ ∆𝐶𝐷𝐴
7. < 𝐴𝐶𝐵 ≅< 𝐶𝐴𝐷
̅̅̅̅ ∥ 𝐵𝐶
̅̅̅̅
8. 𝐴𝐷
9. < 𝐷𝐶𝐴 ≅< 𝐵𝐴𝐶
10. ̅̅̅̅
𝐷𝐶 ∥ ̅̅̅̅
𝐴𝐵
11.𝐴𝐵𝐶𝐷 is a parallelogram
Reasons
1. Given
2. A line segment may be drawn joining 2 points.
3.
4.
5.
6.
7.
8.
9.
10.
11.
Assignment #2: Write the theorem that we have just proven above
Theorem:
2
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.
Complete the exercises below: