2.3c: 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:

2.3c: 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 CCSS:

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

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

Quadrilateral ABCD has vertices A(–2, 1), B(4, 3), C(5, 0), and D(–1, –2). Determine whether ABCD is a rectangle using the Slope Formula. Method 1: Use the Slope Formula, to see if consecutive sides are perpendicular.

Answer: The perpendicular segments create four right angles. Therefore, by definition ABCD is a rectangle. quadrilateral ABCD is a parallelogram. The product of the slopes of consecutive sides is –1. This means that

Method 2: Use the Distance Formula, to determine whether opposite sides are congruent.

Since each pair of opposite sides of the quadrilateral have the same measure, they are congruent. Quadrilateral ABCD is a parallelogram.

The length of each diagonal is Answer: Since the diagonals are congruent, ABCD is a rectangle. Find the length of the diagonals. If we know the shape is a Parallelogram, we can determine if it is a rectangle by the lengths of the diagonals

Quadrilateral WXYZ has vertices W(–2, 1), X(–1, 3), Y(3, 1), and Z(2, –1). Determine whether WXYZ is a rectangle using the Distance Formula.

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?

homework