1. Math 3 Unit 3 Lesson: 2 Parallelograms
Know:
Properties of parallelograms: opposite sides and angles are congruent, diagonals bisect each other.
Rectangle: A special case of parallelogram where the diagonals are congruent.
Be able to:
Prove a quadrilateral is a parallelogram or a rectangle.

2. Learning Resources

3. Opposite sides are congruent.
Opposite sides are parallel.
Opposite angles are congruent.
Diagonals bisect each other.
Consecutive angles are supplementary.

4. Rectangle: A special case of parallelogram where the diagonals are congruent.
All four angles are 90o.
The diagonals are congruent.

5. parallelogram rectangle rhombus square AND: AND: Four congruent sides
Opposite sides are congruent.
Opposite sides are parallel.
Opposite angles are congruent.
Diagonals bisect each other.
Consecutive angles are supplementary.
rectangle
rhombus
AND:
Four congruent sides
AND:
Four right angles
square

6. x = 7 y = 8

7. x = 10 y = 13

8. x = 3

9. Recall:
Distance formula:
Slope formula:
Midpoint formula:

10. Using the slope formula
Prove that quadrilateral A(1,2), B(2,5),C(5,7) and D(4,4) is a parallelogram
Using the slope formula

11. Using the distance formula
Prove that quadrilateral A(1,2), B(2,5),C(5,7) and D(4,4) is a parallelogram
Using the distance formula

12. Using the midpoint formula
Prove that quadrilateral A(1,2), B(2,5),C(5,7) and D(4,4) is a parallelogram
Using the midpoint formula

13. Prove that A(-2,2), B(1,4), C(2,8) and D(-1,6) is a parallelogram

14. Homework More Practice: N.2Properties of parallelograms
N.3Proving a quadrilateral is a parallelogram
Homework