Transcript Classifying Quadrilaterals LESSON 6-1 Additional Examples Judging by appearance, classify ABCD in as many ways as possible. ABCD is a quadrilateral because it has four sides. It.

Classifying Quadrilaterals
LESSON 6-1
Additional Examples
Judging by appearance, classify ABCD in as many
ways as possible.
ABCD is a quadrilateral because it has
four sides.
It is a trapezoid because AB and DC appear
parallel and AD and BC appear nonparallel.
Quick Check
HELP
GEOMETRY
Classifying Quadrilaterals
LESSON 6-1
Additional Examples
Determine the most precise name for the quadrilateral with
vertices Q(–4, 4), B(–2, 9), H(8, 9), and A(10, 4).
Graph quadrilateral QBHA.
First, find the slope of each side.
slope of QB =
9–4
5
=
–2 – (–4)
2
slope of BH =
9–9
=0
8 – (–2)
slope of HA =
4–9
5
=
–
10 – 8
2
slope of QA =
4–4
=0
–4 – 10
BH is parallel to QA because their slopes are equal. QB is not parallel
to HA because their slopes are not equal.
HELP
GEOMETRY
Classifying Quadrilaterals
LESSON 6-1
Additional Examples
(continued)
One pair of opposite sides are parallel, so QBHA is a trapezoid.
Next, use the distance formula to see whether any pairs
of sides are congruent.
QB =
( –2 – ( –4))2 + (9 – 4)2 =
HA =
(10 – 8)2 + (4 – 9)2 =
BH =
(8 – (–2))2 + (9 – 9)2 =
100 + 0 = 10
QA =
(– 4 – 10)2 + (4 – 4)2 =
196 + 0 = 14
4 + 25 =
4 + 25 =
29
29
Because QB = HA, QBHA is an isosceles trapezoid.
HELP
Quick Check
GEOMETRY
Classifying Quadrilaterals
LESSON 6-1
Additional Examples
In parallelogram RSTU, m
m
S = 3x + 50. Find x.
Draw quadrilateral RSTU. Label
RSTU is a parallelogram.
ST || RU
m R + m S = 180
HELP
R = 2x – 10 and
R and
S.
Given
Definition of parallelogram
If lines are parallel, then interior
angles on the same side of a
transversal are supplementary.
GEOMETRY
Classifying Quadrilaterals
LESSON 6-1
Additional Examples
(continued)
(2x – 10) + (3x + 50) = 180
5x + 40 = 180
5x = 140
x = 28
Substitute 2x – 10 for m R and
3x + 50 for m S.
Simplify.
Subtract 40 from each side.
Divide each side by 5.
Quick Check
HELP
GEOMETRY