Download Name Date Common Core Geometry R Hwk #28 Parallelograms 1

Name __________________________
Common Core Geometry R
Date ______________
Hwk #28 Parallelograms
1. Check all properties that apply to each quadrilateral.
Name
Both pairs
of opposite
sides are
parallel.
Both pairs
Both pairs
of
Diagonals
of opposite
opposite
are equal.
angles =.
sides =.
Diagonals
bisect each
other.
Diagonals are
perpendicular All angles
to each
equal.
other.
Diagonals
bisect
opposite
angles.
All sides
equal.
parallelogram
rectangle
rhombus
square
2. Circle the letter of the correct multiple choice answer.
a) Which statement is not always true about a parallelogram?
(1) The diagonals are congruent.
(3) The opposite angles are congruent.
(2) The opposite sides are congruent. (4) The opposite sides are parallel.
b) A parallelogram must be a rectangle if its diagonals
(1) are congruent
(2) bisect each other
(3) are perpendicular to each other (4) bisect the angles whose vertices they connect.
c) If the diagonals of a parallelogram are perpendicular and not congruent, then
the parallelogram is
(1) a rhombus
(2) a square
(3) a rectangle
(4) a trapezoid
d) Which statement is false?
(1) All parallelograms are quadrilaterals.
(2) All rectangles are parallelograms.
(3) All squares are rhombuses.
(4) All rectangles are squares.
Draw a diagram and show all work.
3. In parallelogram STUV, SV = x + 3, VU = 2x - 1, and TU = 4x - 3. Find ST.
4. In rectangle ABCD, diagonals AC and BD are drawn.
m≮BAC = 3x + 4 and m≮ACD = x + 28. Find m≮CAD.
OVER
1
5. PQRS is a parallelogram. m≮SQP = 4x - 2, m≮QSR = 3x + 6, and m≮QPR = 8x - 4.
Solve for x. What specials type of parallelogram is PQRS? Justify your answer.
P
Q
S
R
6. In rectangle ABCD, diagonals AC and BD intersect at E. If AC = 3x + 2, DE = x + 4,
and AD = 2x. Find the length of CD.
7. The degree measures of two opposite angles of a parallelogram are represented by
3x + 40 and x + 70. Is the parallelogram a rectangle? Justify your answer.
8. QRST is a parallelogram. Find x, y, and z.
Q
R
330
5x
T
9. Find x and y so that the quadrilateral is a parallelogram.
2y­5
y+4
27
(3z)0
S
4x­17
(3y+5)0
(5y­13)0
2x­1
2