Name: ________________________________ Unit 10: Quadrilaterals 5/19 or 5/20/15 Geo – Pilch ! Day #2: If it Looks Like a Parallelogram... ! Building off our FIVE true facts about parallelograms, there are SIX ways to prove that a quadrilateral is actually a parallelogram. Let’s list them and label a diagram with each of them. ! #1 ! If a quadrilateral has ______________________________________ then it is a parallelogram. ! ! #2 ! If a quadrilateral has ______________________________________ then it is a parallelogram. ! ! #3 ! If a quadrilateral has ______________________________________ then it is a parallelogram. ! ! #4 ! If a quadrilateral has ______________________________________ then it is a parallelogram. ! ! #5 ! If a quadrilateral has ______________________________________ then it is a parallelogram. ! ! #6 ! If a quadrilateral has ______________________________________ then it is a parallelogram. ! ! ! ! ! Example 1: ! Determine whether each quadrilateral is a parallelogram. JUSTIFY your conclusions with words! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! Example 2: ! Draw a quadrilateral that meets each of the following conditions (one for each letter) that is NOT a parallelogram: ! a. One pair of parallel sides b. One pair of congruent sides c. One pair of parallel sides and one pair of congruent sides Name: ________________________________ Unit 10: Quadrilaterals 5/19 or 5/20/15 Geo – Pilch ! Homework #2: More Practice with Parallelograms ! 1) ! ! ! ! ! ABCD is a parallelogram A = 5x – 24 C = 2x + 15 Find A and A B D D C A = ________________________ D = ________________________ ! ! 2) ! ! ! ! ! ! ! ! ! ! ! 3) ! ! ! ! ! PQRS is a parallelogram S = 5x – 24 R = 2x + 15 Find S and P S = ________________________ P = ________________________ KMOP is a parallelogram. M= (x + 3y)°, O= (x – 4)° and P= (4y – 8)° . Find K. M K O P 4) ! Find x and y in the following parallelogram: ! 25! 2y!+!8! ! ! ! ! 5) ! 3x!+!4! 14! Find x and y in the following parallelogram. ! 6) Determine whether each quadrilateral below is a parallelogram.. If your answer is YES, justify your conclusion with words, using one of our six proofs. ! ! (a) ! ! (c) ! ! ! (b) (d) (e) (f ) ! ! ! ! ! ! (g) (h) ! ! ! 7) ! ! ! ! ! Consider quadrilateral EFGH, below. (Remember – you do NOT yet know it is a parallelogram!!) (a) Solve for x. ! (b) Explain why EFGH is or is not a parallelogram. (Use algebra – don’t measure anything.) ! ! ! 8) ABCD is a parallelogram. AD = 6x and BC = x + 2 . Solve for x and the length of AD. ! ! ! ! ! ! ! ! 2 ! CHALLENGE!! 9) ! ! ! ! ! ! ! ! ! ! ! ! CHALLENGE!! 10) ! ! ! ! ! ! ! ! (you may do this as a two-column proof, or just explain it using words and math.)
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