4 5 Properties of Quadrilaterals Objective Prove quadrilateral

4. 5 Properties of Quadrilaterals 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 Alike: Different: Rhombus vs Square Alike: 4 = sides Opp <‘s = Diagonals perp. Different: 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)

P M L 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 Square Rectangle Note: Sum of the interior <‘s of a quadrilateral = _____

Example: Find the indicated measures for the parallelogram WXYZ W 5 X 2. 2 Z Y m<WXZ = _____ m<ZXY = _____ m<W = _____ XY = _____ m<WZX = _____ Perimeter of WXYZ= _____

Example: E A B D C

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

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

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

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

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

Homework: Practice Worksheet

Parallelograms & Factoring 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 A AD = ______ D C

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

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

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

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

Homework: Practice Worksheet

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

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

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

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