Let’s review the quadrilateral properties we’ve learned so far: All Quadrilaterals Four angles Four sides Angles add to °360 Parallelograms Opposite sides are parallel Opposite sides are congruent Opposite angles are congruent Consecutive angles are supplementary Diagonals bisect each other

Today we’re going to learn about special parallelograms Quadrilaterals – Day 3 Rectangle Today we’re going to learn about special parallelograms Rhombus Square

All Quadrilaterals Parallelogram Rectangle

Rectangle Is a parallelogram Has all the properties of quadrilaterals above it in the flow chart PLUS has the following special properties: Angles are 90° Diagonals are congruent (contractor’s theorem)

All Quadrilaterals Rhombi Parallelograms Rectangles

Rhombus PLUS has the following special properties: Is a parallelogram Has all the properties of quadrilaterals above it PLUS has the following special properties: Sides are congruent Diagonals are perpendicular Diagonals are angle bisectors

Square is the love child of the rectangle and rhombus All Quadrilaterals Rhombus Parallelogram Rectangle Square SQUARE Square is the love child of the rectangle and rhombus

Has all the properties of quadrilaterals above it in the flow chart. SQUARE Dad = Rectangle Mom = Rhombus It gets the congruent sides mom It gets the angles from dad It gets the congruent diagonals from dad It gets perpendicular diagonals from mom It gets angle bisector diagonals from mom

Euler (pronounced ‘oiler’) All Quadrilaterals Rhombus Parallelogram Rectangle Square Venn Diagram Euler (pronounced ‘oiler’) Diagram

I never realized there was so much to learn about quadrilaterals! Whew…. I never realized there was so much to learn about quadrilaterals!

F M D E R 14 in. 20° 26 in. Let’s practice… Find the measures of all the sides, diagonals and angles. Let’s practice… FRED is a rectangle F M D E R 14 in. 26 in. 20° mDM = 15 in.

CRIS is a rhombus Find all angle, side and diagonal measures 28° 8 ft 17 ft 15 ft C S

True or False Every square is a rhombus Every rhombus is a square Every rectangle is a square Every square is a rectangle All rhombi are parallelograms Every parallelogram is a rectangle.

Quadrilaterals Day 4 Kite Trapezoid Trapezium

Convex Quadrilaterals Parallelograms Rectangles Rhombi Square Trapezoid Right Trapezoid Isosceles Trapezoid Trapezium Kite This is what the flow chart will look like at the end of this class.

Properties of a trapezoid A trapezoid has one and only one pair of parallel sides. Two pair of consecutive, supplementary angles.

Midsegment of a trapezoid As the name suggests, a midsegment of a trapezoid is a segment in the middle of a trapezoid. It is parallel with the parallel sides. Behold

Properties of a trapezoid Which is the midsegment? Which is not?

Properties of a trapezoid The length of the midsegment is the average of the lengths of the parallel sides. The midsegment is equidistant from each parallel side. Length 1 Length 1 + Length 2 2 Length 2

Properties of a trapezoid Let’s practice 10 x = 15 16 2x - 4 20 24 2x + 4 CHECK 2x - 4 + 3x + 2 = 2x + 4 2 Does 16 + 32 = 24? 2 3x + 2 32 5x - 2 = 2x + 4 2 If yes, have a personal celebration!! 5x - 2 = 4x + 8 If no, then find your mistake or start over. X = 10

Try this Find the lengths of the parallel segments when x = 2 A B C Z Y M X X + 5 ? AM = 2 BY = 7 CZ = 12 Check to make sure these numbers work… Find ? 2 + 12 = 7 2 ? = X + 10 YEA!!

Try this… If AZ = 31 and CX = 25, find BY BY = 28 C X Y B A Z

Properties of a TRAPEZIUM: A quadrilateral with NO parallel sides. A special Trapezium is a KITE 2 pair of consecutive congruent sides Opposite sides are NOT congruent Only ONE pair of opposite angles are congruent. Diagonals are perpendicular Only ONE diagonal is bisected

White boards…

Your Assignment 6-6 Worksheet