6-2 Parallelograms
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6-2 Parallelograms You classified polygons with four sides as quadrilaterals. • Recognize and apply properties of the sides and angles of parallelograms. • Recognize and apply properties of the diagonals of parallelograms.
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You classified polygons with four sides as quadrilaterals. 6-2 Parallelograms. Recognize and apply properties of the sides and angles of parallelograms. Recognize and apply properties of the diagonals of parallelograms. Parallelogram Probe. Draw diagonals in your parallelogram. - PowerPoint PPT Presentation
Transcript of 6-2 Parallelograms
6-2 Parallelograms
You classified polygons with four sides as quadrilaterals.
• Recognize and apply properties of the sides and angles of parallelograms.
• Recognize and apply properties of the diagonals of parallelograms.
Parallelogram Probe
1. Draw diagonals in your parallelogram.
2. Measure the sides.
3. Measure the diagonals.
4. Measure the diagonal parts.
5. Measure the angles.
Page 403
Page 404
A. CONSTRUCTION In suppose mB = 32, CD = 80 inches, BC = 15 inches. Find AD.
AD = BC Opposite sides of a are .
= 15 Substitution
Answer: AD = 15 inches
B. CONSTRUCTION In suppose mB = 32, CD = 80 inches, BC = 15 inches. Find mC.
Answer: mC = 148
mC + mB = 180 Cons. s in a are supplementary.
mC + 32 = 180 Substitution
mC = 148 Subtract 32 from each side.
C. CONSTRUCTION In suppose mB = 32, CD = 80 inches, BC = 15 inches. Find mD.
Answer: mD = 32
mD = mB Opp. s of a are .
= 32 Substitution
A. 10
B. 20
C. 30
D. 50
A. ABCD is a parallelogram. Find AB.
A. 36
B. 54
C. 144
D. 154
B. ABCD is a parallelogram. Find mC.
A. 36
B. 54
C. 144
D. 154
C. ABCD is a parallelogram. Find mD.
Page 405
Find the following in parallelogram MNOP
d. MP =
e. OP =
f. MQ =
g. NQ =
PMNm.a
MNOmc.OPMmb.
M N
OP
Q
135°
7
15
NP = 21
MO = 11
135°
45°
7
45°
15
5.5
10.5
A. If WXYZ is a parallelogram, find the value of r.
Opposite sides of a parallelogram are .Definition of congruence
SubstitutionDivide each side by 4.
Answer: r = 4.5
B. If WXYZ is a parallelogram, find the value of s.
8s = 7s + 3 Diagonals of a bisecteach other.
Answer: s = 3
s = 3 Subtract 7s from each side.
A. 2
B. 3
C. 5
D. 7
A. If ABCD is a parallelogram, find the value of x.
A. 4
B. 8
C. 10
D. 11
B. If ABCD is a parallelogram, find the value of p.
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
Find the midpoint of
Midpoint Formula
Answer: The coordinates of the intersection of the diagonals of parallelogram MNPR are (1, 2).
Properties of Parallelograms• The opposite sides of a parallelogram are
parallel (by definition).• The opposite angles of a parallelogram are
congruent.• The opposite sides of a parallelogram are
congruent.• The consecutive angles of a parallelogram
are supplementary.• The diagonals of a parallelogram bisect each
other
• What is true about the opposite sides of a parallelogram?
They are parallel and congruent.
• What is true about the opposite angles?
They are congruent.
• What is true about the consecutive angles?
They are supplementary.
• What is true about the diagonals?
They bisect each other.
6-2 Assignment
• Page 407, 9-12,
