Post on 05-Jul-2020
U4 L1 Parallelograms.notebook
Unit 4QUADRILATERALSA polygon with 4 sides
We will use this
for the next 2 class days...
U4 L1
Classifying QuadrilateralsU4 L1
U4 L1 Parallelograms.notebook
Today we will focus mainly on the parallelograms!
Discovering Properites of Parallelograms Using Triangles & Transformations
Use 2 scalene acute triangle
A
B C
Locate the midpoint of side AC
Now, Rotate ΔABC about the midpoint of side AC.
What type of quadrilateral did it create?
Label the image ΔA'B'C'.
List the properties of this parallelogram:
Now, Rotate ΔABC about the midpoint of side AB.
A
B C
Locate the midpoint of side AB
What type of quadrilateral did it create?
CB
A • Opp sides are • Opp angles are • consecutive angles are suppl• diagonals bisect each other
parallelogram
parallelogram
All properties are listed on slide 7
B'
U4 L1 Parallelograms.notebook
Now try with 2 isosceles triangles rotating at the midpoint of the base.
What shape is formed?
What are the properties for this shape?
Try with 2 equilateral triangles.
What type of shape is formed? What properties do we know to be true, and why?
U4 L1 Parallelograms.notebook
Properties of a Parallelogram• Both pairs of opposite sides are • Both pairs of opposite angles are • Consecutive angles are supplementary• Diagonals bisect each other
Definition of Parallelogram: A quadrilateral with both pairs of opposite sides parallel.
All of these properties can be proven using transformations & Congruent Triangles!
Using these property algebraically:
1)
2)
U4 L1 Parallelograms.notebook
Using these property algebraically:
3)
4)
Homework for Monday 12/17
U4 L1 Online
Do the odds and 1st 2 proofs
U4 L1 Parallelograms.notebook
used in proofs
Theorem about Properties of Parallelograms:
Let's prove one of the properties now!
Statement Reason1.2.3.4.5.6.7.8.
1.2.3.4.5.6.7.8.
• Both pairs of opposite sides are
Start here on 12/18
U4 L1 Parallelograms.notebook
• Consecutive Angles of a Parallelogram Are Supplementary
(based on what we know about parallel lines cut by a transversal!)
Here's another proof of the property
A C,≅ ≅B D
Statement Reason1.
2.
3.
1.
2.
3.
A B
CD
Here's another proof of the property• Both pairs of opposite angles are
U4 L1 Parallelograms.notebook
Prove that opposite sides of a parallelogram are congruent.
Proof by Symmetry (Informal – Transformational Approach)
Given: Parallelogram ABCD
A parallelogram has 180 degree rotational symmetry. This means that if I rotate it 180 degrees about the center point E, then
Rotations preserve
Here's another proof of the property
• Diagonals bisect each other
U4 L1 Parallelograms.notebook
Given: Parallelogram ABCD
Prove that the diagonals bisect each other.
A parallelogram has 180 degree rotational symmetry. This means that if I rotate it 180 degrees about the center point E, then AE _____ and BE ____ . Rotations preserve distance. This means that E is the midpoint of AC and BD. If E is the Midpoint, then the line segments bisected each other!
Homework for Tues 12/18
U4 L1Do the evens and the last 2 proofs
U4 L1 Parallelograms.notebook