Post on 28-Dec-2015
transcript
Parallelogram – both pairs of opposite sides are parallel
Rhombus – four congruent sides
Special Quadrilaterals
Rectangle – four right angles Square – four congruent sides and four congruent angles
Kite – two pairs of adjacent sides are congruent and no opposite sides are congruent
Trapezoid – Exactly one pair of parallel sides Isosceles Trapezoid – the nonparallel
sides are congruent.
Classifying a Quadrilateral
Judging by appearance, classify ABCD in as many ways as possible.
Quadrilateral and Trapezoid
Relationships Among Special Quadrilaterals
Quadrilateral
No parallel sides
Kite Trapezoid
One pair of parallel sides
Isosceles Trapezoid
Parallelogram
Rectangle Rhombus
Square
Two pairs of parallel sides
Using the Properties of Special Quadrilaterals
In parallelogram RSTU, m R = 2x – 10 and m S = 3x + 50. Find x.
Closing . . .
ABCD is a square. Which classifications from this lesson apply to a square? Which do not apply?
A square is:
A square is not:
quadrilateral, parallelogram, rectangle, rhombus
trapezoid, kite
Directions:• When the slide appears say the best name for the quadrilateral aloud.
• Try to beat the computer by saying the answer before the computer in 4 seconds.
Key to remembering these!
We’re going to be learning a lot of similar looking theorems.
Draw a few pictures to see what happens.
Thm 6-1
Opposite sides of a parallelogram are congruent.
Other Properties of Parallelograms: Opposite sides are parallel Consecutive angles are supplementary
Thm 6-4
If three (or more) parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal.
Thm 6-5
If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.
Thm 6-6
If one pair of opposite sides of a quadrilateral is both congruent and parallel, then the quadrilateral is a parallelogram.
Finding Values for Parallelograms
Find values of x and y for which ABCD must be a parallelogram.
x = 18 and y = 89
Thm 6-7
If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
Thm 6-8
If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
Is the Quadrilateral a Parallelogram?
Determine whether the quadrilateral is a parallelogram. Explain.