My Favorite No D EB 7 AE 10

My Favorite No!! D EB = 7 AE = 10 DE = DC Find AD E C B A

Chapter 4 Quadrilaterals

Quadrilateral

Parallelogram

Objectives To identify any quadrilateral, by name, as specifically as you can, based on its characteristics To use characteristics of quadrilaterals to solve for sides and/or angles To write proofs involving all types of quadrilaterals.

Special Quadrilaterals There are several special types of quadrilaterals. They are classified based on their sides or angles.

Quadrilateral Family Tree Kite Right Trapezoid

Quadrilateral Family Tree Right Trapezoid A quadrilateral is a polygon with 4 sides.

Quadrilateral a quadrilateral is a polygon with 4 sides.

Right Trapezoid

A parallelogram is a quadrilateral with two pairs of parallel sides.

Parallelogram Definition: a quadrilateral with two pairs of parallel sides

Parallelogram: A diagonal of a parallelogram separates it into two congruent triangles

Parallelogram: The opposite angles of a parallelogram are congruent.

Parallelogram: Two consecutive angles of a parallelogram are supplementary. 1 2

Parallelogram: The opposite sides of a parallelogram are congruent.

Parallelogram: The diagonals of a parallelogram bisect each other.

Parallelogram: In a parallelogram with unequal pairs of consecutive angles, the longer diagonal lies opposite the obtuse angle.

Parallelogram: 5 ways showing a Quadrilateral is a Parallelogram: 1) Both pairs of opposite sides are parallel 2) If both pairs of opposites sides are congruent 3) If one pair of opposites sides are both parallel and congruent 4) If the diagonals bisect each other 5) If both pairs of opposite angles are congruent.

Parallelogram:

Parallelogram:

Kite A kite is a quadrilateral with NO parallel sides but 2 pairs of adjacent congruent sides.

Kite No sides are parallel! Definition: A kite is a quadrilateral with 2 pairs of consecutive congruent sides (adjacent congruent sides) 4 in. 2 in.

Kite One pair of opposite sides are congruent.

Kite

Something else you need to know: The line segment that joins the midpoint of two sides of a triangle has a length equal to one-half the length of the third side.

Try one: If AB = 12. 7 Find ED

Maybe two: If DE = 2 x + 1 AB = 5 x - 1 Find: x, DE and AB

EXIT TICKET!!!

Right Trapezoid

A rectangle is a parallelogram that is equiangular.

Rectangle Definition: a parallelogram with 4 congruent angles, all 90 degrees.

Rectangle Characteristics: 1) The diagonals are congruent

Rectangle A B AC = 17 BC = 15 Find AB Find BD D C

Rectangle

Rectangle

Right Trapezoid

A square is a specific case of both a rhombus AND a rectangle, equiangular and equilateral.

Square Definition: a regular parallelogram An equilateral rectangle An equiangular rhombus

A rhombus is a parallelogram that is equilateral.

Rhombus Definition: a parallelogram with 4 congruent sides. 4 in.

Rhombus Characteristics: 1) The diagonals of a rhombus are perpendicular. 4 in.

Rhombus

A trapezoid is a quadrilateral with only one pair of parallel sides. Right Trapezoid

A trapezoid is a quadrilateral with only one pair of parallel sides.

Trapezoid trapezoids Definition: a quadrilateral with exactly one pair of parallel sides.

Right Trapezoid An isosceles trapezoid is a trapezoid with the legs congruent.

Right Trapezoid A right trapezoid has one leg ┴ to the // lines

Isosceles Trapezoid: Right Trapezoid a trapezoid with congruent legs. Legs are the non-parallel sides A trapezoid with parallel sides perpendicular to one leg.