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Chapter 8: Quadrilaterals

Chapter 8: Quadrilaterals. 8.3.1 Show that a Quadrilateral is a Parallelogram. How do we determine a quadrilateral is a parallelogram. Same as last section: Opposite sides are congruent Diagonals bisect Opposite angles are congruent Two pairs of parallel sides New to this section:

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Chapter 8: Quadrilaterals

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  1. Chapter 8: Quadrilaterals 8.3.1 Show that a Quadrilateral is a Parallelogram

  2. How do we determine a quadrilateral is a parallelogram • Same as last section: • Opposite sides are congruent • Diagonals bisect • Opposite angles are congruent • Two pairs of parallel sides • New to this section: • One pair of opposite sides are congruent and parallel

  3. Prove the new one: • Let AB || DC AB = DC • Then ABC  DCB by AIA • Since BC = CB • By SAS ABC  DCB • CPCTC says AC = DB • then ABCD is a parallelogram A B C D

  4. Use a co-ordinate plane to determine parallelogram: • A(-3 , 3) , B(2 , 5), C(5 , 2), D(0 , 0)

  5. Find the value of x • So that ABCD is a parallelogram • AE= 5x – y - 3 EB= 12 – x - 2y • ED= x + y EC= 5x + y A B E D C

  6. Homework • p. 526 • 3 – 6, 8 – 11, 15, 16, 19 – 21, 25, 32

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