### 15-3 quadrilateral hw key

```1. Which statement is not always true about a rectangle?
) he diagonals are perpendicular
3) The adjacent sides are perpendicular.
2) The opposite sides are congruent.
4) Two sets of opposite sides are parallel.
2. In the diagram below of rhombus ABCD, mZC= 100
What is mZDBC?
1000
D
c
3. In the accompanying diagram of parallelogramABCD, mZA = 2x —10and mZB = 5x+15. Find the m<CBA.
c
L C.Bh
q s=tso
t2SàlS
—10)0
+ 15) 0
15
4) Quadrilateral ABCD has diagonals AC and BD. Which information
is not sufficient to prove ABCD is a parallelogram?
(l) AC and BD bisect each other.
(2) AB CD and BC AD
3) AB CD and AB Il CD
(4) AB CD and BC IlAD
S(XWL
di
00
5. In the diagram below, quadrilateralSTAR is a rhombus with diagonals SA and TR intersecting atE. ST —3x+ 30,
3z, TE- 5z+5, AE-4z- 8, my-RTA- sy- 2,andmZTAS- 9Y+8.
3x+30
s
SR- 8x- 5,
Ÿ6)-S
8x-5
b) Solve for RT
c) Solve formZTAS
THs
6. Given: ABCD is a parallel
ram with diagonals
nd B Intersecting at E.
know
p
c
D
Prove: AAED
ACEB
6 hC
ShS
Ñasùns
8b bisec+
aces
z
òP
seroicv
7. In the coordinate plane, the vertices of ARST are
and T(—5,6).
State the coordinates of point P such that quadrilateral RSTP is a rectangle.
Yo heip
so
. •
For
SR's
Prove that your quadrilateral RSTP is a rectangle.
[The use of the set of axes below is optional.]
- -.10
s
3
opp. sldes
PST? is
8) In which quadrilateral are the diagonals not congruent to each other?
(a) isosceles trapezoid
(b)hombus
(c) rectangle
(d) square
9) Which statement is true?
(a) Every square is a rhombus.
(b) Every rhombus is a square.
(c) Every trapezoid is a parallelogram.
(d) Every parallelogram is a rectangle.
know
pard
vs
10) Which is an example of a quadrilateral whose adjacent sides are always perpendicular?
(a) a parallelogram
(b) a rhombus
(c) an isosceles trapezoid
(d) rectangle
11)
In rhombus ABCD, with diagonals AC and DB,
the
to
10
diaow„ls
c
If the length ofdiagonal AC is 12, what is the
length of DB?
2 16
44
3)
accompanyingdiagramof parallelogram
12. In
ABCD, mZB = Sr, and mZC=2x + 12. Find the
number ofdegrees in ZD.
c
Bshy)
x? Z (of
```