Session 31 Check your homework with a neighbor. Which property justifies the statement? 1. If A B and B C, then A C. 2. If M N, then N M. 3. If 1 = 80, and m1 = m2, then m2 = 80. Transitive property of congruence Symmetric property of congruence Substitution property of equality
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Session 31 Check your homework with a neighbor. Which property justifies the statement? 1.If A B and B C, then A C. 2.If M N, then.
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Session 31 Check your homework with a neighbor.
Which property justifies the statement?
1. If A B and B C, then A C.
2. If M N, then N M.
3. If 1 = 80, and m1 = m2, then m2 = 80.
Transitive property of congruence
Symmetric property of congruence
Substitution property of equality
AGENDA
1. Discuss hw
2. Notes 6.2 & 6.3
3. Practice
Fri. 11th
Quiz & 6.4
Tues. 14th
6.5 & 6.6
Thurs. 16th
6.7
HW Check1. Use the number of sides to
identify the polygon.
2. Is #1 concave or convex, explain your answer.
3. Use the information in the diagram to find the mA.
4. Use the information in the diagram to solve for x.
Concave A37
153
8x 3x – 1
2x + 13
143
15
Nonagon
Questions over your hw?p. 325 1 - 30, 37 - 39, 41 - 46
6.2 Properties of Parallelograms
Parallelogram• A quadrilateral with both pairs of opposite sides parallel
IF a quadrilateral is a parallelogram then…
• Opposite sides are congruent
(THM 6.2)
Opposite sides are congruent
IF a quadrilateral is a parallelogram then…
• Opposite angles are congruent
(THM 6.3)
Opposite angles are congruent
IF a quadrilateral is a parallelogram then…
• Consecutive angles are supplementary
(THM 6.4)
Consecutive angles are supplementary.
ADD UP TO 180°
IF a quadrilateral is a parallelogram then…
• Diagonals bisect each other
(THM 6.5)
Diagonals bisect each other.
This cuts the diagonals into two equal parts.
ABCD is a parallelogram. Find the lengths and the angle measures.
1. AD
2. EC
3. mADC
4. mBCD
B 8 C
A D
6545
E
5
85
110
70
5. Find the value of each variable in the parallelogram.
4y
x = 5
2y42x – 6
y = 30
6. Find the value of each variable in the parallelogram.
10x = 6
3y + 12x – 1
y = 3 x + 5
6.3 Proving Quadrilaterals are Parallelograms
How do you know if you have one?
1.BOTH pairs of opposite sides are parallel2.BOTH pairs of opposite sides are congruent
3. BOTH pairs of opposite angles are congruent
4.ONE angle is supplementary to BOTH consecutive angles
5.diagonals BISECT each other
6. ONE pair of opposite sides are CONGRUENT & PARALLEL
60 120
120
6 6
50°
130°
Show that A(2, 0), B(3, 4), C(-2, 6), and D(-3, 2) is a parallelogram.
• One way is to show that opposite sides are parallel by finding every sides’ slopes.
• Another way is to find the distances of both pairs of opposite sides.
Show that A(2, 0), B(3, 4), C(-2, 6), and D(-3, 2) is a parallelogram.