6.2 Properties of Parallelograms
OBJECTIVE: To discover properties of parallelograms
Use parallel lines (If lines are parallel, same-side interior angles are ________________________ )
to find the missing angles in the parallelogram below:
C-28: The consecutive angles in a parallelogram are _________________________.
C-29: The opposite angles in a parallelogram are _________________________.
Example 1: Find the value of x in parallelogram ABCD. Then find mA.
Investigation: Determine which triangles are congruent. What do you notice about point T?
∆𝐵𝑇𝐶 ≅ ∆____________ by _________
∆𝐴𝐵𝑇 ≅ ∆____________ by _________
̅̅̅̅ ≅ ______________ by _______________.
̅̅̅̅ ≅ ______________ and 𝑇𝐶
So 𝐵𝑇
8
So T is a ________________ of ___________ and ___________.
C-30: The diagonals of a parallelogram _______________each other.
Example 2: Find the values of x and y in parallelogram KLMN.
3
1 2
7
4
6 5
Check for Understanding: Summary Properties of Parallelograms

Opposite sides are ________________________. (Definition)

Opposite sides are ________________________.

Opposite angles are ________________________.

Consecutive angles are ________________________.

Diagonals ________________________ each other.
Check for Understanding: Properties of Special Types of Quadrilaterals
C-31: If three (or more) parallel lines cut off congruent segments on one transversal,
then they cut off ___________ segments on every transversal.
⃡ ∥ 𝐶𝐷
⃡ ∥ 𝐸𝐹
̅̅̅̅ ≅ 𝐶𝐸
̅̅̅̅
⃡ and 𝐴𝐶
If: 𝐴𝐵
Then: ________________________
Example 4: In the figure, ⃡𝐷𝐻 ∥ ⃡𝐶𝐺 ∥ ⃡𝐵𝐹 ∥ ⃡𝐴𝐸 . Find EH.