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.

Learning Resources

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

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

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

x = 7 y = 8

x = 10 y = 13

x = 3

Recall: Distance formula: Slope formula: Midpoint formula:

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

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

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

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

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