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Geometry B Bellwork

Geometry B Bellwork. 1) State whether the quadrilateral is a parallelogram. Explain your reasoning. 6.5 Trapezoids and Kites. Geometry. Using properties of trapezoids.

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Geometry B Bellwork

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  1. Geometry B Bellwork 1) State whether the quadrilateral is a parallelogram. Explain your reasoning.

  2. 6.5 Trapezoids and Kites Geometry

  3. Using properties of trapezoids • A trapezoid is a quadrilateral with exactly one pair of parallel sides. The parallel sides are the bases. A trapezoid has two pairs of base angles. For instance in trapezoid ABCD D and C are one pair of base angles. The other pair is A and B. The nonparallel sides are the legs of the trapezoid.

  4. Trapezoid Theorems Theorem 6-15 • The base angles of an isosceles trapezoid are congruent. • A ≅ B, C ≅ D

  5. Trapezoid Theorems Theorem 6-16 • The diagonals of an isosceles trapezoid are congruent. • ABCD is isosceles, AC ≅ BD.

  6. Geometry B Bellwork 2) State the definition of a trapezoid. Label its parts.

  7. Kite theorems Theorem 6-17 • The diagonals of a kite are perpendicular • AC  BD

  8. EX. Given an isosceles trapezoid.Find the measure of each angle… 1) 3 2 77° 1

  9. OYO… Given an isosceles trapezoid find the measures of the missing angles 2) 2 3 1 49 °

  10. EX. Given a kite, find the measures of the numbered angles 45° 1 3 65º 2

  11. OYO…Given a kite, find the measures of the numbered angles 52° 1 3 4 2 65º

  12. Solve for x. 3) 4) 60° (3x + 15)° 2x ° (x + 6)°

  13. Ex. 2: Using properties of trapezoids • Show that ABCD is a trapezoid. • Compare the slopes of opposite sides. • The slope of AB = 5 – 0 = 5 = - 1 0 – 5 -5 • The slope of CD = 4 – 7 = -3 = - 1 7 – 4 3 • The slopes of AB and CD are equal, so AB ║ CD. • The slope of BC = 7 – 5 = 2 = 1 4 – 0 4 2 • The slope of AD = 4 – 0 = 4 = 2 7 – 5 2 • The slopes of BC and AD are not equal, so BC is not parallel to AD. • So, because AB ║ CD and BC is not parallel to AD, ABCD is a trapezoid.

  14. The midsegment of a trapezoid is the segment that connects the midpoints of its legs. Midsegment of a trapezoid

  15. The midsegment of a trapezoid is parallel to each base and its length is one half the sums of the lengths of the bases. MN║AD, MN║BC MN = ½ (AD + BC) Theorem 6.17: Midsegment of a trapezoid

  16. Find the midsegment AD= 28, BC=12 MN = ½ (AD + BC) EX. Midsegment of a trapezoid

  17. LAYER CAKE A baker is making a cake like the one at the right. The top layer has a diameter of 8 inches and the bottom layer has a diameter of 20 inches. How big should the middle layer be? Ex. 3: Finding Midsegment lengths of trapezoids

  18. Use the midsegment theorem for trapezoids. DG = ½(EF + CH)= ½ (8 + 20) = 14” Ex. 3: Finding Midsegment lengths of trapezoids E F D G D C

  19. Ex. 5: Angles of a kite • Find mG and mJ in the diagram at the right. SOLUTION: GHJK is a kite, so G ≅ J and mG = mJ. 2(mG) + 132° + 60° = 360°Sum of measures of int. s of a quad. is 360° 2(mG) = 168°Simplify mG = 84° Divide each side by 2. So, mJ = mG = 84° 132° 60°

  20. Reminder: • Quiz after this section

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