Lesson 8.3: Show that a Quadrilateral is a Parallelogram

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6.3 Proving that a Quadrilateral is a Parallelogram

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Presentation transcript:

Lesson 8.3: Show that a Quadrilateral is a Parallelogram Geometry

Theorem 8.7: Side Congruence Theorem If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram. Converse of Theorem 8.3

Theorem 8.8: “Angle Congruence Theorem” If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram. Converse of Theorem 8.4

Theorem 8.9: “Congruent Parallel Theorem” If one pair of opposite sides of a quadrilateral are congruent AND parallel, then the quadrilateral is a parallelogram.

Theorem 8.10: “Diagonal Bisect Theorem” If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

Summary: Ways to Prove a Quadrilateral is a Parallelogram Show both pairs of opposite sides are parallel. [Definition of Parallelogram] Show both pairs of opposite sides are congruent. [Side Congruence Th.] Show both pairs of opposite angles are congruent. [Angle Congruence Th.] Show one pair of opposite sides are congruent and parallel. [Congruent Parallel Th.] Show the diagonals bisect each other. [Diagonal Bisect Th.]

Examples What theorem can you use to show that the quadrilateral is a parallelogram?

Check Your Progress What theorem can you use to show that the quadrilateral is a parallelogram?

Warm-Up Find the slope of the line that passes through the points Find the midpoint of the segment that begins at and ends at . Find the distance between the points .

Angle Congruence Th. Side Congruence Th. Diagonal Bisect Th. Congruent Parallel Th.

Board Points 30 point grade Each time you go to the board and complete a problem, explain you problem to the class and have the correct work and answer, you will receive 6 points. You need at least 5 visits to the board in order to receive the 30 points. Any additional boards points after 5 will be worth 3 extra credit points per problem. You will have until May 5th to go up 5 times (most likely one chance per week).

Lesson 8.3: Show that a Quadrilateral is a Parallelogram (part 2) Geometry

Prove that a Quadrilateral is a Parallelogram on a Coordinate Plane Given the ordered pairs of the vertices of a quadrilateral, you can prove whether the quadrilateral is a parallelogram or not. Some Concepts to remember: Slope Distance Formula Midpoint Formula

How to Prove a Quadrilateral is a Parallelogram on a Coordinate Plan DEFINITION OF PARALLELOGRAM Find Slope of all 4 sides. Opposite sides need to have equal Slope. SIDE CONGRUENCE THEOREM Find distance of all 4 sides. Opposite sides need to be equal in distance. CONGRUENT PARALLEL THEOREM Find Slope of one pair of opposite sides. They need to be equal. Find distance of the same pair of opposite sides. They need to be equal.

Homework WED 3/16: THU 3/17 Workbook Pg. 151 Textbook Pg. 523 #1-10 (all) Textbook Pg. 523 #2-7 (all) THU 3/17 Worksheet Packet 8.1: #7-25 (odd) 8.2: #5, 11-19 (odd) 8.3: #1-13 (odd)