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8.2 use properties of parallelograms

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8.2 use properties of parallelograms

1. 1. 8.2 Use Properties of Parallelograms 8.2 Bell Thinger 1. Find the value of x. ANSWER 60 2. Find the coordinates of the midpoint of AB with endpoints A(–2, 6) and B(10, 4). ANSWER (4, 5) 3. Find the distance between (–2, 6) and (10, 4). ANSWER 2 37
2. 2. 8.2
3. 3. 8.2 Example 1 ALGEBRA Find the values of x and y. ABCD is a parallelogram by the definition of a parallelogram. Use Theorem 8.3 to find the value of x. AB = CD Opposite sides of a x + 4 = 12 In . Substitute x + 4 for AB and 12 for CD. x=8 By Theorem 8.4, are Subtract 4 from each side. A C,or m ABCD, x = 8 and y = 65. A=m C. So, y ° = 65°.
4. 4. 8.2 Guided Practice 1. Find FG and m ANSWER G. 8, 60° 2. Find the values of x and y. ANSWER 25, 15
5. 5. 8.2
6. 6. 8.2 Example 2 Desk Lamp As shown, part of the extending arm of a desk lamp is a parallelogram. The angles of the parallelogram change as the lamp is raised and lowered. Find m BCD when m ADC = 110°. SOLUTION By Theorem 8.5, the consecutive angle pairs in ABCD are supplementary. So, m ADC + m BCD = 180°. Because m ADC = 110°, m BCD =180° –110° = 70°.
7. 7. 8.2
8. 8. 8.2 Example 3 SOLUTION By Theorem 8 .6, the diagonals of a parallelogram bisect each other. So, P is the midpoint of diagonals LN and OM . Use the Midpoint Formula. Coordinates of midpoint P of OM = ( 7 + 0 , 4 + 0 ) = ( 7 , 2 ) 2 2 2 ANSWER The correct answer is A.
9. 9. 8.2 Guided Practice Find the indicated measure in 3. NM 4. KM ANSWER 5. m JKLM. 2 6. m JML ANSWER ANSWER 70° 4 KML ANSWER 40°
10. 10. Exit 8.2 Slip Part 1 3 minutes 1. Find the values of a and b in the parallelogram. ANSWER 42, 26 2. Find the measure of the parallelogram. ANSWER 116o K in
11. 11. Exit 8.2 Slip Part 2 3 minutes Find the indicated measures in parallelogram ABCD. 3. m BCD ANSWER 43 4. If BE = 9, find BD. ANSWER 18
12. 12. 8.2 Pg 538-540 #3, 8, 10, 14, 39