6.2 Properties of Parallelograms

```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 mοA.
Investigation: Determine which triangles are congruent. What do you notice about point T?
βπ΅ππΆ ≅ β____________ by _________
βπ΄π΅π ≅ β____________ by _________
ΜΜΜΜ ≅ ______________ by _______________.
ΜΜΜΜ ≅ ______________ and ππΆ
So π΅π
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
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Opposite sides are ________________________. (Definition)
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Opposite sides are ________________________.
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Opposite angles are ________________________.
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Consecutive angles are ________________________.
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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.
β‘ β₯ πΆπ·
β‘ β₯ πΈπΉ
ΜΜΜΜ ≅ πΆπΈ
ΜΜΜΜ
β‘ and π΄πΆ
If: π΄π΅
Then: ________________________
Example 4: In the figure, β‘π·π» β₯ β‘πΆπΊ β₯ β‘π΅πΉ β₯ β‘π΄πΈ . Find EH.
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