6.3. Parallelograms http://www.ck12.org
Example C
Show that the diagonals ofF GHJbisect each other.
The easiest way to show this is to find the midpoint of each diagonal. If it is the same point, you know they intersect
at each other’s midpoint and, by definition, cuts a line in half.
Midpoint ofF H:(
− 4 + 6
2
,
5 − 4
2
)
= ( 1 , 0. 5 )
Midpoint ofGJ:(
3 − 1
2
,
3 − 2
2
)
= ( 1 , 0. 5 )
Watch this video for help with the Examples above.
MEDIA
Click image to the left for more content.CK-12 Foundation: Chapter6ParallelogramsB
Concept Problem Revisited
By the Parallelogram Diagonals Theorem, the fountain is going to be 34 feet from either endpoint on the 68 foot
diagonal and 25 feet from either endpoint on the 50 foot diagonal.
Vocabulary
Aparallelogramis a quadrilateral with two pairs of parallel sides.
Guided Practice
1.SANDis a parallelogram,SY= 4 x−11 andY N=x+10. Solve forx.
- Find the measures ofaandbin the parallelogram below:
- Ifm^6 B= 72 ◦in parallelogramABCD, find the other three angles.
Answers:
- Because this is a parallelogram, the diagonals bisect each other andSY∼=Y N.
SY=Y N
4 x− 11 =x+ 10
3 x= 21
x= 7- Consecutive angles are supplementary so 127◦+m^6 b= 180 ◦which means thatm^6 b= 53 ◦.aandbare alternate
interior angles and since the lines are parallel (since its a parallelogram), that means thatm^6 a=m^6 b= 53 ◦.