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Section 5.1 - Parallelograms

Section 5.1 - Parallelograms. 11/15 Remember: a quadrilateral is any 4-sided polygon. Parallelograms are a type of quadrilateral with both pairs of opposite sides parallel. Recall: The sum of the interior angles of a parallelogram (and quadrilateral) is 360 ْ .

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Section 5.1 - Parallelograms

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  1. Section 5.1 - Parallelograms 11/15 Remember: a quadrilateral is any 4-sided polygon. Parallelograms are a type of quadrilateral with both pairs of opposite sides parallel. Recall: The sum of the interior angles of a parallelogram (and quadrilateral) is 360ْ. If you know a shape is a parallelogram, then it has 4 big properties (theorems).

  2. Section 5.1 - Parallelograms • Parallelograms are named by 4 vertices, start with any and go around. C l o c k w i s e ABCD A B BCDA CDAB DABC D C C o u n t e r C l o c k w i s e CBAD DCBA ADCB BADC

  3. Section 5.1 - Parallelograms Theorem #1: The opposite sides of a parallelogram are congruent.

  4. Section 5.1 - Parallelograms Theorem #1: The opposite sides of a parallelogram are congruent. Proving Theorem #1:

  5. Section 5.1 - Parallelograms Theorem #2: The opposite angles of a parallelogram are congruent

  6. Section 5.1 - Parallelograms Theorem #2: The opposite angles of a parallelogram are congruent Proving Theorem #2: Using the proof from Theorem #1, we know (given): and by ASA Therefore, with CPCTC, <B = <D. And because <1 = <2 and <3 = <4, by using angle addition postulate and substitution, we can also conclude that <A = <C. ~ ~ ~ ~

  7. Section 5.1 - Parallelograms Theorem #3: The diagonals of a parallelogram bisect each other.

  8. Section 5.1 - Parallelograms Theorem #3: The diagonals of a parallelogram bisect each other. Proving Theorem #3: Using the proof from Theorem #1 and #2, we know (given): ΔABC = ΔCDA and ΔDBA = ΔBDC ~ ~ 5 8 O 7 6 ~ ~ 5 8 O ~ O 7 6

  9. Section 5.1 - Parallelograms Theorem #4: The same-side interior angles (consecutive angles) of a parallelogram are supplementary angles. C A D B ﮮA +ﮮ B = 180ْ ﮮC +ﮮ A = 180ْ ﮮC +ﮮ D = 180ْ ﮮD +ﮮ B = 180ْ

  10. Parallelograms – We Do 18 A B w x The following quadrilaterals are parallelograms. Example 1 Solve for w,x,y,z. Example 2 Solve for j,k,l,m,n. y 10 w = 115º x = 65º 115º y = 10 z = 18 D C z E F 55º 65º j = 60º k = 55º n 40º l l = 120º m = 40º j m n = 20º k H G

  11. Parallelograms – You Do • Textbook practice: Pg 168 #2-8

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