1. Special Quadrilaterals
Unit 6: Lesson #2
Special Quadrilaterals
Warm-up:
Quadrilateral Vocab
(on the front table)

3. Quadrilateral Vocab ۞ A quadrilateral is a _4_ sided polygon.
Name Definition Picture
PARALLELOGRAM Opposite sides are //
RHOMBUS Parallelogram (TWO pairs of // sides)
All sides are congruent

4. Quadrilateral Vocab Name Definition Picture
RECTANGLE Parallelogram (TWO pairs of // sides) All angles are exactly 90.
SQUARE Parallelogram (TWO pairs of // sides)
All sides are congruent .
All angles are exactly 90.

5. Quadrilateral Vocab KITE 2 pairs of congruent consecutive sides.
TRAPEZOID Exactly one pair of
parallel sides.
ISOSCELES TRAPEZOID
Trapezoid (Exactly one pair of parallel sides.)
Non-parallel sides are congruent .

7. Example #1 a) Classify each figure in as many ways as possible,
b) Determine the most precise name for each figure.
A) B) C)
quadrilateral
quadrilateral
quadrilateral
trapezoid
parallelogram
rectangle
parallelogram
isosceles
trapezoid
rhombus
square

8. Example #1
For the examples below, determine if the statement is “True” or “False”.
(D) Every rectangle is a square.
(E) Every isosceles trapezoid is a quadrilateral.
False
True

9. Example #2
A) The figure is a kite. x = _______
x + 2
2x – 1
2x – 1 = x + 2
x - 1 = 2
x = 3

10. Example #2 B) The figure is a rectangle. m = _______
Each angle of a rectangle is 90
(12m – 6)0
12m – 6 = 90
12m = 96
m = 8

11. Example #2 x = 20 C) The figure is a parallelogram. x = _______
Opposite sides are parallel.
(4x – 5)0
(2x + 65)0
Same-side interior angles are supplementary
2x x – 5 = 180
6x + 60 = 180
6x = 120
x = 20

12. Example #2 3b + 2 5a + 4 4b – 2 3a + 8 D) The figure is a rhombus.
All sides are equal.
5a + 4 = 3a + 8
2a = 4
a = 2
4b – 2 = 3b + 2
b = 4

13. MG = 5/7 GB -9/0 = Und. BD 1/7 DM -5/0 = Und. 6 – 1 4 – (-3) -3 – 6
Example #3
A) Vertices: M(-3, 1), G(4, 6), B(4, -3), D(-3, -4)
The figure appears to be a …. M G B D
Trapezoid
Let’s prove it …
Side Slopes: MG GB BD DM
= 5/7
-9/0 = Und.
1/7
-5/0 = Und.
6 – 1
4 – (-3)
-3 – 6
4 – 4
-4 – (-3)
-3 – 4
One Pair of Parallel sides.
-4 – 1
-3 – (-3)

14. Example #3 4 – 0 -1 – 5 1 – -3 -3 – 3 4 – 1 -1 – -3 -3 – 0 3 – 5
B) Vertices: T(-1, 4), A(5, 0), J(3, -3), W(-3, 1)
The figure appears to be a ….
RECTANGLE T A J W
Let’s prove it …
Slopes:
TA =
WJ =
TW =
JA =
= 4/-6 = -2/3
= 3/2
= -3/-2 = 3/2
4 – 0
-1 – 5
1 – -3
-3 – 3
Slopes of adjacent side lengths are opposite reciprocals, so sides form right angles.
TAJW is a rectangle.
4 – 1
-1 – -3
-3 – 0
3 – 5

15. Homework Time!