EXAMPLE 2 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°.

EXAMPLE 3 Standardized Test Practice 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.

GUIDED PRACTICE for Examples 2 and 3 Find the indicated measure in 3. NM JKLM. SOLUTION By Theorem 8. 6, the diagonals of a parallelogram bisect each other. So, N is the midpoint of diagonals KM. KN = NM 2 = NM Substitute

GUIDED PRACTICE for Examples 2 and 3 Find the indicated measure in 4. KM JKLM. SOLUTION KM = KN + NM By theorem 8. 6 KM = 2 + 2 Substitute KM = 4 Add

GUIDED PRACTICE for Examples 2 and 3 Find the indicated measure in 5. m JML JKLM. SOLUTION By Theorem 8. 5, the consecutive angle pairs in JKLM are supplementary. So, m KJM + m Because m JML = 180°. KJM = 110°, m JML =180° – 110° = 70°.

GUIDED PRACTICE for Examples 2 and 3 Find the indicated measure in 6. m KML JKLM. SOLUTION m JML = m KMJ + m 70° = 30° + m 40° = m KML KNL Substitute Subtract