1. YES NO--- not right angles Determine whether PQRS is a rectangle.
Warm-up 2/7/12
Determine whether PQRS is a rectangle.
1. P(2,3) Q(5,9) R (11,6) S( 8,0)
2. P(-1,4) Q(3,6) R (9,-3) S(5,-5)
YES
NO--- not right angles

2. Homework Answers Rectangles

3. ST= 5
VT=12
VS=14
Perimeter = 34
Area = 60 7. 8. 9.
10. AT=11,VA=11,AS=11
11. (4 – 2)180 = 360

4. Remember if LMNO is a rectangle. Opposite sides are
congruent, all angles are 90°, Diagonals are congruent and
bisect each other.
x = 90, x = 10
13. 3x + 21 = 72, x = 17
14. OZ = ½ LN, 5x = ½ (30), 5x = 15, x = 3
15. LZ = ½ MO, 2(x- 4) = ½ (8), x - 4 = 2, x = 6
16. Slopes of edges: AB = undefined, AD = 0,
CD = undefined, BC = 0
Slope of diagonals: BD = -4/5, AC = 4/5 (diagonals are not
perpendicular)
AB // CD, AD // BC (same slopes)
AB ⊥ AD and CD ⊥ BC
ABCD is a rectangle, because opposites sides are parallel and corner angles are right angles.

5. A = (19)(8) = 152
18. A = (6)(12) = 72
19. b = A = (6)(8) = 48
b = 100
b = 64
b = 8
20. A = 186

6. 4.5 Rhombus Essential Questions:
(1). What are the characteristics of a rhombus?
(2). How can we prove the shape is a rhombus?

7. Define Rhombus:
A quadrilateral with four
congruent sides.
Since all the edges of a rhombus are
congruent, opposite edges are congruent.
A quadrilateral with opposite edges
congruent is defined to be a parallelogram.
Hence, all __________ are parallelograms.
rhombi

8. The five properties of parallelograms also
pertain to rhombuses (rhombi):
Opposite edges of a rhombus are ________.
Opposite angles of a rhombus are ________.
Consecutive interior angles of a rhombus
are ______________.
The diagonals of a rhombus ______ each other.
parallel
congruent
congruent
supplementary
bisect

9. In addition to the five properties above, there are two additional properties.
Investigation:
Step 1: Copy ABCD on a sheet of patty paper.
Step 2: Fold the patty paper in half so that B
overlays D. Crease the patty paper firmly.
Unfold.
Step 3: Fold the patty paper in half so that A
overlays C. Crease the patty paper
firmly. Unfold.
The creases in the patty paper represent the diagonals AC and BD. Are the diagonals perpendicular?
YES

10. Step 4: Fold the patty paper in half again where AC is. the crease
Step 4: Fold the patty paper in half again where AC is the crease. Does AC bisect A and C?
YES
Step 5: Fold the patty paper in half again where BD is the crease. Does BD bisect B and D?
YES

11. From this investigation we can conclude:
The diagonals of a rhombus are____________.
The diagonals of a rhombus bisect a pair of
_________ angles
perpendicular
opposite

12. Answer each question using rhombus ADCB pictured below.
(1). If AB = 18 cm, then
CD = ___ cm, and
BC = _____ cm, and AD = ____cm.
(2). If then
and C 18 18 18
60o
120o
120o

13. intersect at point X, then m AXB = _____, m 90o 90o AXD = _____,
(3). If
and
intersect at point X, then m
AXB = _____, m
90o
90o
AXD = _____,
and m
BXC = _____.
90o
(4). If
and
intersect at point X,
and mA = 80o, then mBAX = _____,
mDAX = ______, mADX = ____,
mCDX = ______.
40o
40o
50o
50o

14. 4 6 (5). If BX = 2 cm, then BD = __ cm.A 4
(5). If BX = 2 cm, then BD = __ cm.
(6). If AC = 12 cm, then AX = __ cm. D B 6 C
(7).
║____;
║____;
(8).
 ___
(9). If AB = 8 ft then the perimeter of the
rhombus is ______ ft. 32

15. 360o (10). The sum of the measures of the interior
angles of the rhombus is ______.
(11). Is the rhombus a quadrilateral? T or F
(12). Is the rhombus a parallelogram? T or F
(13). Is the rhombus a rectangle? T or F
360o T T F

16. How to prove a quadrilateral is a Rhombus:
parallelogram
1st Prove it is a __________________ (using one of the five ways to prove a quadrilateral is a parallelogram) 2nd Show (1) Diagonals are _________________ OR (2) Diagonals __________ corner angles OR (3) 2 Adjacent sides are _______________ (which means all 4 sides will be ______ )
perpendicular
bisect
Congruent
equal

17. (14). The coordinates of the Quadrilateral are
W(-3,-3), X(1,-6), Y(5,-3) and Z(1,0).
a. Find the slope of WX
b. Find the slope of XY
c. Find the slope of YZ
d. Find the slope of WZ

18. (14). The coordinates of the Quadrilateral are W(-3,-3), X(1,-6), Y(5,-3) and Z(1,0). e. Find the slope of WY (the slope of the diagonal) f. Find the slope of XZ (the slope of the diagonal)
We proved that both pairs of opposite sides are parallel,
therefore, it is a parallelogram. We also proved the
diagonals are perpendicular. So it is a RHOMBUS!

19. Since a rhombus is a parallelogram, we can
use the formula A = bh to find the area of a
rhombus. There is an additional formula
for the area of a rhombus as well: A = ½ d1d2
Find the area of each rhombus.
8.4 ft2
3.5 ft
15. A = ________
1.2 ft
1.2 ft
3.5 f t
A = ½ d1● d2
A = ½ (7)(2.4)
A = 8.4 ft2

20. 96 cm2 16. A = ________ a2 + b2 = c2 62 + b2 = 102 36+b2 = 100
A = ½ d1● d2
b2 = 64
A = ½ (12)(16)
b = 8
A = 96 cm2