QUADRILATERALS

QUADRILATERALS Parallelograms Rectangles Rhombi Squares Trapezoids Kites

Definition: Opposite Sides are parallel. Parallelograms Definition: Opposite Sides are parallel. A D B C

Opposite sides are congruent. Parallelograms Opposite sides are congruent. A D B C

Opposite angles are congruent. Parallelograms Opposite angles are congruent. A D B C

Diagonals bisect each other. Parallelograms Diagonals bisect each other. A D B C M

Parallelograms Consecutive Angles are supplementary. A D B C

Parallelograms A D B C M

Special Parallelograms RECTANGLES A D B C Definition: Quadrilateral with Four right angles. M Diagonals are congruent.

Special Parallelograms RECTANGLES A D B C Since the diagonals of a rectangle are congruent, AC=BD M

Special Parallelograms RHOMBUSES A D B C Definition: Quadrilateral with Four congruent sides. 2 3 1 4 M 5 8 6 7 Diagonals bisect opposite angles. Diagonals are perpendicular.

Special Parallelograms RHOMBUSES A D B C 20 in Find the following: mBCM AC m AMD AD m DCB BD 12 in = 67 23 = 24 in M = 90 = 20 in 𝑨𝑴 𝟐 + 𝑩𝑴 𝟐 = 𝑨𝑩 𝟐 𝟏𝟐 𝟐 + 𝑩𝑴 𝟐 = 𝟐𝟎 𝟐 = 134 𝟏𝟒𝟒+ 𝑩𝑴 𝟐 =𝟒𝟎𝟎 = 32 in 𝑩𝑴 𝟐 =𝟐𝟓𝟔 𝑩𝑴 =𝟏𝟔

Definition: It’s a Rectangle Rhombus Special Parallelograms SQUARES A D B C Definition: It’s a Rectangle Rhombus Rectangle & a Rhombus M SQUARES have ALL the properties of parallelograms, rectangles & rhombuses.

Quadrilateral with exactly one pair of parallel sides. Trapezoids Definition: Quadrilateral with exactly one pair of parallel sides. B A D C Bases are parallel. A & D are supp. and  B & C are supp.

Segment that joins the midpoints of the legs of a trapezoid. Trapezoids A D B C Midsegment: Segment that joins the midpoints of the legs of a trapezoid. X Y XY is the midsegment. Midsegment is ll to bases and ½ measure of the sum of bases.

Trapezoid that has congruent legs. Isosceles Trapezoids A D B C Definition: Trapezoid that has congruent legs. Each pair of Base angles are congruent. Legs are congruent. A  B and  D  C. Diagonals are congruent:

Quadrilateral that has opposite sides congruent. Kites B C D A Definition: Quadrilateral that has Two pair of congruent Adjacent sides and no opposite sides congruent. Diagonals are . One pair of opposite Angles are congruent.

Pythagorean Theorem is often used to find measures. Kites B C D A One diagonal bisects the other. Pythagorean Theorem is often used to find measures.