2.2b: Quadrilaterals M(G&M)–10–2 Makes and defends conjectures, constructs geometric arguments, uses geometric properties, or uses theorems to solve problems.

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Presentation transcript:

2.2b: Quadrilaterals M(G&M)–10–2 Makes and defends conjectures, constructs geometric arguments, uses geometric properties, or uses theorems to solve problems involving polygons GSE’s - Rectangle

POLYGONS Quadrilaterals Parallelograms RECTANGLES Has ALL the properties of the shapes above it

In Addition to all those: Rectangles also have: A 1) Congruent Diagonals 2) All 4 angles are right What can we do to prove these on the coordinate plane? B R N Use Distance Formula for AB and RN Use slope to find if each consecutive side is opposite reciprocals

Solve for x and the m<ADB and m<BDC

X, and the length of RB, VQ

Quadrilateral RSTU is a rectangle. If and find x. The diagonals of a rectangle are congruent, Definition of congruent segments Substitution Subtract 6x from each side. Add 4 to each side.

Quadrilateral LMNP is a rectangle. Find x and y

Determine whether each statement is True or False. Explain If the quadrilateral is a rectangle, then it is a parallelogram If the quadrilateral is a parallelogram, then it is a rectangle. If a parallelogram has congruent diagonals, then it is a rectangle If a quadrilateral has congruent diagonals, then it is a rectangle True, all rectangles are parallelograms False, not all parallelograms are rectangles, they could be other shapes as well. True, by definition, a parallelogram with congruent diagonals is a rectangle False, a 4 sided figure (quadrilateral) could have congruent diagonals and not be a rectangle

If you wanted to install a ceiling fan in your rectangular family room, Find where it would be in the room?

The foundation for your house was poured, and you measured the outside walls to Be 40’ by 24’. Does this make it rectangular? Why or why not?

To determine if a parallelogram is a rectangle: A) show the two diagonals are equal by the distance formula Or B) show the four corners are perpendicular (90 degrees) by slopes

Prove if it’s a rectangle. Easiest way = Find the length of the 2 diagonals (AC and BD)

homework