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Warm up on a little piece of paper:

Warm up on a little piece of paper:. Find the values of the variables. . 4.8. 4.5. a – 1.4. 7y - 3. 4y + 6. 2a - 7. b – 2.3. 5y + 1.4. 6.5 Trapezoids and kites. LEQ: What are the special properties of trapezoids and kites?. Theorem 6-15

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Warm up on a little piece of paper:

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  1. Warm up on a little piece of paper: Find the values of the variables. 4.8 4.5 a – 1.4 7y - 3 4y + 6 2a - 7 b – 2.3 5y + 1.4

  2. 6.5 Trapezoids and kites LEQ: What are the special properties of trapezoids and kites?

  3. Theorem 6-15 If a trapezoid is isosceles, then each pair of base angles is congruent. A ≅ B, C ≅ D Using properties of trapezoids A B C D

  4. Proof of part of thm. 6-15 Prove that m<C=m<D A B Construct BE so that it’s parallel to AC 1 C E D 1.) AC=BD, AB//CD 1.) Given 2.) AC=BE 2.) Opposite sides of parallelograms are congruent 3.) BE=BD 3.) Transitive Property/substitution 4.) m<D=m<1 4.) Isosceles Triangle Thm. 5.) m<1=m<C 5.) Corresponding Angles 6.) m<C=m<D 6.) Transitive/Substitution

  5. PQRS is an isosceles trapezoid. Find mS, mQ, mR and QR. Ex. 1: Using properties of Isosceles Trapezoids P Q 50° 2.6 S R

  6. 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? (the top of the middle layer must be exactly halfway between the top of the first and 3rd layers)

  7. Recall median of a triangle • Half the distance of the base

  8. Different!! The median of a trapezoid is the segment that connects the midpoints of its legs. Thm 6-18 says the median: Is parallel to each base: MN║AD, MN║BC Has a length equal to the average of the base lengths MN = ½ (AD + BC) Theorem 6-18: Median of a trapezoid

  9. Example: Both are medians 4 x 5.8 x + 3 8.6 22 Find the value of x. Find the value of x.

  10. Theorem 6-16 A B C D The diagonals of an isosceles trapezoid are congruent. Why??*Bonus* proof due Monday Ex: Find the value of x if AC = 2x + 10 and BD = 3x + 4

  11. Kites What other quadrilaterals share this characteristic? Kites Recap: What are the requirements in order to be a kite? *note*: one pair of opp. <‘s is bisected (the diag. that splits the congruent legs) Theorem 6-17: The diagonals of a kite are _____________.

  12. Example: 32˚ 46˚ Find the measures of the numbered angles. Find the measures of the numbered angles.

  13. What rules can we derive for kites? 1.) diagonals are perpendicular 2.)adjacent sides congruent, but not all sides congruent

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