6-3 Proving Quads are Parallelograms

6-3 Proving Quads are Parallelograms

Learning Objective: I can determine whether or not a quadrilateral is a parallelogram.

In 6-2 we learned about the theorems and properties of parallelograms, in this section we will learn about the CONVERSES to those theorems.

Therefore, if we can determine that a quadrilateral has certain properties (the properties we learned about on Tuesday and Wednesday), then the quadrilateral IS a parallelogram.

Open Ended

List the 5 properties of a parallelogram we learned in the previous section:

Theorem 6-8 (Converse of 6-3)

If both pairs of opposite sides of a quadrilateral are ≅, the the quadrilateral is a parallelogram.

More converses....

​(Converse to 6-4)

​(Converse to 6-5)

Example 1: Finding Values of Parallelograms

Step 1: Find x.

3x - 5 = 2x+1
x = 6

Step 2: Find y.

x+2 = y
6+2 = y
y = 8

​For what value of y must PQRS be a parallelogram?

Example 2: Finding Values of Parallelograms

Step 1: Find x.

4x+13 + 12x+7 = 180
16x + 20 = 180
16x = 160
x = 10

Step 2: Find y.

3y-2 + y+10 = 180
4y+8=180
4y = 172
y = 43

​For what value of a and y must EFGH be a parallelogram?

Multiple Choice

For what values of x and y must ABCD be a parallelogram?

• y=39, x = 3

• y=19.5, x = 3

• y=39, x = 21

• y=19.5, x = 21

Multiple Choice

For what values of x and y must ABCD be a parallelogram?

• x = 3

• x = 5

• x = -1/3

• x = 2

​Last two! For today...

​(Converse of Theorem 6-6)

Multiple Choice

Determine if the quadrilateral is a parallelogram and justify.

• opposite sides parallel (def.)

• opposite sides congruent (6.1)

• opposite angles congruent (6.2)

• diagonals are mutual bisectors (6.3)

• Not a parallelogram.

Multiple Choice

Determine if the quadrilateral is a parallelogram and justify.

• opposite sides parallel (def.)

• opposite sides congruent (6.1)

• opposite angles congruent (6.2)

• one set of sides is parallel and congruent (6.4)

• Not a parallelogram.

Multiple Choice

Determine if the quadrilateral is a parallelogram and justify.

• opposite sides parallel (def.)

• opposite sides congruent (6.1)

• opposite angles congruent (6.2)

• one set of sides is parallel and congruent (6.4)

• Not a parallelogram.

Multiple Choice

Determine if the quadrilateral is a parallelogram and justify.

• opposite sides parallel (def.)

• diagonals are mutual bisectors (6.3)

• opposite angles congruent (6.2)

• one set of sides is parallel and congruent (6.4)

• Not a parallelogram.

Deciding Whether a Quad is a Parallelogram
Can you prove that the quad is a parallelogram based on the given information? Explain.

Open Ended

Can you prove that the quadrilateral is a parallelogram based on the given information? Explain.

Open Ended

Can you prove that the quadrilateral is a parallelogram based on the given information? Explain.

Open Ended

Can you prove that the quadrilateral is a parallelogram based on the given information? Explain.

Once you have finished the practice problems, get out a piece of paper and complete the following problems as an exit ticket (you will turn this in):

​Do you remember what a biconditional statement is???

Your sentence should have "if and only if" in it!