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2.3: Quadrilaterals

- parallelograms. 2.3: Quadrilaterals. CCSS:. GSE’s. M(G&M)–10–2 Makes and defends conjectures, constructs geometric arguments, uses geometric properties, or uses theorems to solve problems involving polygons. Quadrilaterals. 4-Sided polygon. Parallelogram.

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2.3: Quadrilaterals

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  1. - parallelograms 2.3: Quadrilaterals CCSS: GSE’s M(G&M)–10–2 Makes and defends conjectures, constructs geometric arguments, uses geometric properties, or uses theorems to solve problems involving polygons

  2. Quadrilaterals • 4-Sided polygon

  3. Parallelogram • A Quadrilateral with both pairs of opposite sides parallel A B C D

  4. Properties of Parallelograms Find all the angle measures Inside of the parallelogram 50 Write some conjectures about the angles in a parallelogram

  5. Properties of Every Parallelogram: • Both pairs of opposite sides are congruent. • Both pairs of opposite angles are congruent. • Consecutive adjacent angles are supplementary. • Diagonals bisect each other.

  6. Example Find every angle measure in the figure.

  7. RSTU is a parallelogram. Find and y. Example 2-2a

  8. Example 2 Parallelogram ABCD, find x. A B 2x+12 26 C D 22

  9. MULTIPLE-CHOICE TEST ITEM What are the coordinates of the intersection of the diagonals of parallelogram MNPR, with vertices M(–3, 0), N(–1, 3), P(5, 4), and R(3, 1)? A B C D Read the Test ItemSince the diagonals of a parallelogram bisect each other, the intersection point is the midpoint of Example 2-3a

  10. MULTIPLE-CHOICE TEST ITEM What are the coordinates of the intersection of the diagonals of parallelogram LMNO, with verticesL(0, –3), M(–2, 1), N(1, 5), O(3, 1)? A BC D Example 2-3c Answer: B

  11. Parallelogram ABDC Find the equation of the Lines of DC and BA. What do we know should be true?

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