 # Objective: Prove quadrilateral conjectures by using triangle congruence postulates and theorems Warm-Up: How are the quadrilaterals in each pair alike?

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Objective: Prove quadrilateral conjectures by using triangle congruence postulates and theorems Warm-Up: How are the quadrilaterals in each pair alike? How are they different? Parallelogram vs Square Rhombus vs Square Alike: Different: Alike: Different: 4 = sides Opp <‘s = Diagonals perp. Sq has 4 right <‘s

Quadrilateral: Any four sided polygon. Trapezoid: A quadrilateral with one and only one pair of parallel sides. Parallelogram: A quadrilateral with two pairs of parallel sides. Rhombus: A quadrilateral with four congruent sides. Rectangle: A quadrilateral with four right angles. Square: A quadrilateral with four congruent sides and four right angles.

PROPERTIES OF SPECIAL QUADRILATERALS: PARALLELOGRAMS: Both pairs of opposite sides are parallel Both pairs of opposite sides are congruent Both pairs of opposite sides angles are congruent Consecutive angles are supplementary Diagonals bisect each other A diagonal creates two congruent triangles (it’s a turn – NOT a flip)

M L P G Theorem: A diagonal of a parallelogram divides the parallelogram into two congruent triangles.

PROPERTIES OF SPECIAL QUADRILATERALS: RECTANGLES: Rectangles have all of the properties of parallelograms plus: Four right angles Congruent Diagonals Perpendicular Sides

PROPERTIES OF SPECIAL QUADRILATERALS: RHOMBUSES: Rhombuses have all of the properties of parallelograms plus: Four congruent sides Perpendicular diagonals Diagonals bisect each other

PROPERTIES OF SPECIAL QUADRILATERALS: SQUARES: Squares have all of the properties of parallelograms, rectangles & rhombuses.

Parallelogram Rhombus Rectangle Square Note: Sum of the interior <‘s of a quadrilateral = _____

Example: Find the indicated measures for the parallelogram WXYZ m<WXZ = _____ m<W = _____ m<ZXY = _____ XY = _____ m<WZX = _____ Perimeter of WXYZ= _____ W X Z Y 2.2 5

Example: AB D E C

Example: Find the indicated measure for the parallelogram A B C D m<A = ______

Example: Find the indicated measure for the parallelogram Q R S T QR = ______ 6x-2 10 x+4

Example: Find the indicated measure for the parallelogram C F E D CD = ______ x-7

Example: Find the indicated measure for the parallelogram M P O N m<N = ______

Example: Find the indicated measure for the parallelogram E G F H m<G = ______

Homework: Practice Worksheet

Objective: Identify the missing component of a given parallelogram through the use of factoring. Warm-Up: What is the first number that has the letter “a” in its name?

Example: Find the indicated measure for the parallelogram B D C A AD = ______

Example: Find the indicated measure for the parallelogram D G F E m<E = ______

Example: Find the indicated measure for the parallelogram Q R S T QR = ______

Example: Find the indicated measure for the parallelogram P S R Q m<R = ______

Collins Writing: How could you determine the sum of the interior angles of a quadrilateral?

Homework: Practice Worksheet

L G P M 4 2 3 1 Given: Prove: Parallelogram PLGM with diagonal LM STATEMENTS REASONS

Given: Prove: Parallelogram ABCD with diagonal BD STATEMENTS REASONS C A D 2 1 5 4 B 3 6

Given: Prove: Parallelogram ABCD with diagonal BD STATEMENTS REASONS Theorem: Theorem: Opposite sides of a parallelogram are congruent.

Given: Prove: Parallelogram ABCD with diagonals BD & AC STATEMENTS REASONS Theorem: Theorem: Opposite angles of a parallelogram are congruent.