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## 6.6 Trapezoids and Kites

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**6.6 Trapezoids and Kites**Last set of quadrilateral properties**Start with the trapezoid**• Parallel sides are called bases**Start with the trapezoid**• Non parallel sides are called legs.**Start with the trapezoid**• Since one pair is parallel**Start with the trapezoid**• Since one pair is parallel Angles on the same leg are supplementary.**Now for the special**• Isosceles trapezoid is a trapezoid whose legs are congruent.**And now for the proof, drawing in perpendiculars**A B C D E F**Why is ?**A B C D E F**Remember,**A B C D E F**Why is ?**A B C D E F**As a result, ACE BDF by?**A B C D E F**C D by…**A B C D E F**As a result, A B by…**A B C D E F**Theorem 6-19: If a quadrilateral is an isosceles trapezoid,**then each pair of base ’s is . A B C D E F**Make sure you can…**• Given one angle of an isosceles trapezoid, find the remaining 3 angles.**AC BD because?**A B E C D**C D by?**A B E C D**If we want to prove ’s ACD and BCD are congruent, what**do they share? A B E C D**ACD BCD by**A B E C D**AD BC by**A B E C D**Theorem 6-20: If a quadrilateral is an isosceles trapezoid,**then its diagonals are A B E C D**The return of midsegments** A midsegment of a trapezoid connects the midpoints of the legs (non parallel sides) and is the mean value of the 2 bases (parallel sides)**The return of midsegments**A midsegment of a trapezoid connects the midpoints of the legs (non parallel sides) and is the mean value of the 2 bases (parallel sides)**In addition…**A midsegment of a trapezoid connects the midpoints of the legs (non parallel sides) and is the mean value of the 2 bases (parallel sides)**In addition…**Much like triangles, the midsegment is parallel to the sides it does not touch.**So find its length?**• Add the bases and divide by 2.**Working backwards**• Formula:**Working backwards**• Formula: • Midsegment =**Plug in the length of the midsegment.**• Formula: • Midsegment =**Plug in the length of a base.**• Formula: • Midsegment =**Solve for the remaining base**• Formula: • Midsegment =**Solve for the remaining base**• Or • Arithmetically, multiply the length of the midsegment by 2 and subtract the length of the given base.**Here’s a problem I enjoy.**• Given an isosceles trapezoid whose midsegment measures 50 cm and whose legs measures 24 mm. Find its perimeter.