Chapter 6 – Quadrilaterals Lesson 6.2 – Parallelograms ...

Chapter 6 – QuadrilateralsLesson 6.2 – ParallelogramsParallelogram: A quadrilateral with opposite sides parallel.Example 1: Prove that if a parallelogram has two consecutive sides congruent, ithas four congruent sides.Given: ABCD; ADABProve: AD AB BC CDStatementsReasons1. ABCD; AD AB 1. Given2. AD BC, AB CD3. AD AB BC CD2. Def parallelogram3. Transitive Prop of CongruenceLesson 6.2 – Page 1

NOW TRY THIS: Prove that if and are thediagonals of ABCD, BEC DEA and BEA BCDEC.Given: ABCDProve: BEC DEAAEDBEA DECStatementsReasons1. ABCD 1. Given2.BCA DAC, DBC BDA,BAC DCA, ABD CBD2. If 2 || lines are cut by atransversal then each pair ofalternate interior ’s are .3. BC DA , AB CD 3. Def of parallelogram4. BEC DEA, BEA DEC 4. ASAExample 2: Quadrilateral RSTU is aparallelogram. Find mURT, mRST, and y.m URT3y =18y = 640, m RST=122,NOW TRY THIS: Quadrilateral LMNP is a parallelogram. FindmPLM, mLMN, and d.2d22d 11m PLM 108m LMN 72Lesson 6.2 – Page 2

Example 3: What are the coordinates of the intersection of the diagonals ofparallelogram MNPR with vertices M(-3, 0), N(-1, 3), P(5, 4) and R(3, 1)?1. Draw a picturemidpoint of NR (1,2)NOW TRY THIS: What are the coordinates of the intersection of the diagonalsof parallelogram LMNO with vertices L(0, -3), M(-2, 1), N(1, 5), and O(3, 1)?1. Draw a picture.1midpoint of MO ( ,1)2Example 4: How would you write a proof for Theorem 6.8You would use the def on parallelogram to get alt int angles congruent, then thereflexive property. By ASA, the triangles would be congruent.Lesson 6.2 – Page 3