6-3 Proving that a Quadrilateral is a Parallelogram Objective: To determine whether a quadrilateral...
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Transcript of 6-3 Proving that a Quadrilateral is a Parallelogram Objective: To determine whether a quadrilateral...
![Page 1: 6-3 Proving that a Quadrilateral is a Parallelogram Objective: To determine whether a quadrilateral is a parallelogram Essential Understanding: You can.](https://reader035.fdocuments.net/reader035/viewer/2022071706/56649d1b5503460f949f120d/html5/thumbnails/1.jpg)
6-3Proving that a
Quadrilateral is a Parallelogram
Objective: To determine whether a quadrilateral is a parallelogram
Essential Understanding: You can decide whether a quadrilateral is a parallelogram if its sides, angles and diagonals have certain properties
![Page 2: 6-3 Proving that a Quadrilateral is a Parallelogram Objective: To determine whether a quadrilateral is a parallelogram Essential Understanding: You can.](https://reader035.fdocuments.net/reader035/viewer/2022071706/56649d1b5503460f949f120d/html5/thumbnails/2.jpg)
Opposite angles are congruent
Review
Opposite sides are parallel
Opposite sides are congruent
Opposite angles are congruent
Consecutive angles are supplementary
Diagonals bisect each other
![Page 3: 6-3 Proving that a Quadrilateral is a Parallelogram Objective: To determine whether a quadrilateral is a parallelogram Essential Understanding: You can.](https://reader035.fdocuments.net/reader035/viewer/2022071706/56649d1b5503460f949f120d/html5/thumbnails/3.jpg)
Theorems 6-9 and 6-10 are the converses of Theorems 6-4 and 6-5, respectively. They use angle relationships to conclude that a quadrilateral is a parallelogram.
![Page 4: 6-3 Proving that a Quadrilateral is a Parallelogram Objective: To determine whether a quadrilateral is a parallelogram Essential Understanding: You can.](https://reader035.fdocuments.net/reader035/viewer/2022071706/56649d1b5503460f949f120d/html5/thumbnails/4.jpg)
![Page 5: 6-3 Proving that a Quadrilateral is a Parallelogram Objective: To determine whether a quadrilateral is a parallelogram Essential Understanding: You can.](https://reader035.fdocuments.net/reader035/viewer/2022071706/56649d1b5503460f949f120d/html5/thumbnails/5.jpg)
Example:
For what value of y must PQRS be a parallelogram?
Step 1: Find x.
3x – 5 = 2x + 1
X – 5 = 1
X = 6
Step 2: Find y.
y = x + 2y = 6 + 2
y = 8
![Page 6: 6-3 Proving that a Quadrilateral is a Parallelogram Objective: To determine whether a quadrilateral is a parallelogram Essential Understanding: You can.](https://reader035.fdocuments.net/reader035/viewer/2022071706/56649d1b5503460f949f120d/html5/thumbnails/6.jpg)
and FINALLY
6-3 p. 372:7-15