2.2b: quadrilaterals m(g&m)–10–2 makes and defends conjectures, constructs geometric...
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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?
BR
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.
908523 xx
90108 x808 x10x
322)10(3
588)10(5
NLPm
MLNm
5y
306y
3226y
AnglesInterior Alternate
PLNMNL
58 32
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?
12
12
xx
yy
212
212 )()( yyxx
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)
212
212 )()( yyxx
homework