WarmUp 1 Exercises EXAMPLE Use properties of parallelograms

Warm-Up 1 Exercises EXAMPLE Use properties of parallelograms 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 x + 4 = 12 x=8 By Theorem 8. 4, ANSWER Opposite sides of a . Substitute x + 4 for AB and 12 for CD. Subtract 4 from each side. A In are C, or m A=m C. So, y ° = 65°. ABCD, x = 8 and y = 65.

Warm-Up Exercises GUIDED PRACTICE 1. Find FG and m ANSWER for Example 1 G. 8, 60° 2. Find the values of x and y. ANSWER 25, 15

Warm-Up 2 Exercises EXAMPLE Use properties of parallelograms 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°.

Standardized Test Practice Warm-Up 3 Exercises EXAMPLE 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 +2 0 , 4 +2 0 ) = ( 7 , 2 ) 2 ANSWER The correct answer is A.

Warm-Up Exercises GUIDED PRACTICE for Examples 2 and 3 Find the indicated measure in JKLM. 3. NM JML ANSWER 5. m 2 4. KM ANSWER 6. m 4 70° KML ANSWER 40°

Warm-Up Exercises Daily Homework Quiz 1. Find the values of a and b in the parallelogram. ANSWER 42, 26 2. Find the measure of ANSWER 116 o K in the parallelogram.

Warm-Up Exercises Daily Homework Quiz Find the indicated measures in parallelogram ABCD. 3. m BCD ANSWER 43 o 4. If BE = 9, find BD. ANSWER 18