Chapter 6.2 and 6.3
Parallelograms and
Tests for Parallelograms
Parallelogram
O A parallelogram is a quadrilateral with both
pairs of opposite sides parallel
Concept 1
Use Properties of Parallelograms
A. CONSTRUCTION In
suppose
mB = 32, CD = 80 inches, BC = 15 inches.
Find AD.
Use Properties of Parallelograms
B. CONSTRUCTION In
suppose
mB = 32, CD = 80 inches, BC = 15 inches.
Find mC.
Use Properties of Parallelograms
C. CONSTRUCTION In
suppose
mB = 32, CD = 80 inches, BC = 15 inches.
Find mD.
A. ABCD is a parallelogram. Find AB.
A. 10
B. 20
C. 30
D. 50
B. ABCD is a parallelogram. Find mC.
A. 36
B. 54
C. 144
D. 154
C. ABCD is a parallelogram. Find mD.
A. 36
B. 54
C. 144
D. 154
Concept 3
Use Properties of Parallelograms and Algebra
A. If WXYZ is a parallelogram, find the value of r.
Use Properties of Parallelograms and Algebra
B. If WXYZ is a parallelogram, find the value of s.
Use Properties of Parallelograms and Algebra
C. If WXYZ is a parallelogram, find the value of t.
A. If ABCD is a parallelogram, find the value of x.
A. 2
B. 3
C. 5
D. 7
B. If ABCD is a parallelogram, find the value of p.
A. 4
B. 8
C. 10
D. 11
C. If ABCD is a parallelogram, find the value of k.
A. 4
B. 5
C. 6
D. 7
Parallelograms and Coordinate Geometry
What are the coordinates of the intersection of the
diagonals of parallelogram MNPR, with vertices
M(–3, 0), N(–1, 3), P(5, 4), and R(3, 1)?
Since the diagonals of a parallelogram bisect each other,
the intersection point is the midpoint of
What are the coordinates of the intersection of the
diagonals of parallelogram LMNO, with vertices
L(0, –3), M(–2, 1), N(1, 5), O(3, 1)?
A.
B.
C.
D.
Concept 1
Identify Parallelograms
Determine whether the quadrilateral is a parallelogram.
Justify your answer.
Which method would prove the
quadrilateral is a parallelogram?
A. Both pairs of opp. sides ||.
B. Both pairs of opp. sides .
C. Both pairs of opp. s .
D. One pair of opp. sides both ||
and .
Use Parallelograms and Algebra to Find Values
Find x and y so that the quadrilateral is a parallelogram.
Opposite sides of a parallelogram are congruent.
Find m so that the quadrilateral is a parallelogram.
A. m = 2
B. m = 3
C. m = 6
D. m = 8
Concept 3
Parallelograms and Coordinate Geometry
COORDINATE GEOMETRY
Quadrilateral QRST has vertices
Q(–1, 3), R(3, 1), S(2, –3), and
T(–2, –1). Determine whether the
quadrilateral is a parallelogram.
Justify your answer by using the
Slope Formula.
If the opposite sides of a quadrilateral are parallel, then it
is a parallelogram.
Graph quadrilateral EFGH with vertices E(–2, 2), F(2, 0),
G(1, –5), and H(–3, –2). Determine whether the
quadrilateral is a parallelogram using the distance
formula and slope formula.
A. yes
B. no