# Hotmath

Make a concept map (a tree diagram or a Venn diagram) to organize these quadrilaterals: rhombus, rectangle, square, trapezoid.

Consider the parallelogram shown alongside. Complete the statement given below, giving reasons.

Δ
*
OAD
*
is congruent to?

Draw a pair of parallel lines by tracing along both edges of your ruler. Draw a transversal. Use your compass to bisect each angle of a pair of alternate interior angles. What shape is formed? Can you explain why?

The figure shown consists of two parallelograms,
*
WXYZ
*
and
*
ABCD
*
. Find the measure of angle
*
WAD
*
.

*
If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram
*
.

Sketch and label a diagram. List what is given and what is to be proved. Then write a two–column proof of the above statement.

Consider rectangle
*
JKLM
*
shown in the figure.

If
*
JL
*
= 6
*
y
*
– 21 and
*
MN
*
= 2
*
y
*
+ 9, find
*
y
*
.

Find the perimeter of quad.
*
LNOK
*
if
*
L
*
,
*
M
*
, and
*
N
*
are the midpoints of the sides of Δ
*
TKO
*
in the given figure.

The angles of a quadrilateral measure 2
*
x
*
,
*
x
*
*
+
*
30,
*
x
*
+ 50, and 2
*
x
*
– 20. The quadrilateral could be:

(a) square (b) parallelogram (c) trapezoid

I. (a) or (b)

II. (b) or (c)

III. (a) alone

IV. (b) alone

V. (c) alone

Quadrilateral
*
PQRS
*
has vertices
*
P
*
(–2, 2),
*
Q
*
(5, 9),
*
R
*
(8, 6), and
*
S
*
(1, –1). Is
*
PQRS
*
a rectangle? Determine using slopes.

Using straightedge and compass, construct an isosceles trapezoid
*
PQRS
*
with legs of length
*
y
*
units.

The vertices of quadrilateral
*
ABCD
*
are

*
A
*
= (–2, –4),
*
B
*
= (2, –7),
*
C
*
= (6, –4), and
*
D
*
= (2, –1). Determine whether
*
ABCD
*
is a square, a rhombus, a rectangle, or a parallelogram. List all names that apply.

In the figure,
and
are the bases of trapezoid
*
ABCD
*
. Find the coordinates of median
for
*
ABCD
*
. Show that
||
.

In the figure shown,
and
are the bases of trapezoid
*
PQRS
*
and
. Prove that
*
PQRT
*
is a parallelogram.

*
A
*
,
*
B
*
,
*
C
*
, and
*
D
*
are the midpoints of the sides of isosceles trapezoid
*
PQRS
*
. What type of quadrilateral is
*
ABCD
*
?