# 6.6Trapezoids and Kites

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6.6 Trapezoids and Kites

6.6Trapezoids and KitesLast set of quadrilateral propertiesTerminology:Terminology:TrapezoidKiteTerminology:TrapezoidQuadrilateral with exactly one pair of parallel sides.KiteTerminology:TrapezoidQuadrilateral with exactly one pair of parallel sides.KiteQuadrilateral with two pairs of consecutive congruent sides, none of which are parallel.Start with the trapezoid

Now for the specialIsosceles trapezoid is a trapezoid whose legs are congruent.And now for the proof, drawing in perpendicularsA B

C D E FA B

C D E FA B

C D E FA B

C D E FAs a result, ACE BDF by?A B

C D E FC D byA B

C D E FAs a result, A B byA B

C D E FTheorem 6-19: If a quadrilateral is an isosceles trapezoid, then each pair of base s is .A B

C D E FMake sure you canMake sure you canGiven one angle of an isosceles trapezoid, find the remaining 3 angles.Application: page 390 Problem 2

Focusing on 1 section

AC BD because? A B

EC DC D by? A B

EC DIf we want to prove s ACD and BCD are congruent, what do they share? A B

EC DACD BCD by A B

EC DAD BC by A B

EC DTheorem 6-20: If a quadrilateral is an isosceles trapezoid, then its diagonals are A B

EC DThe return of midsegmentsThe return of midsegmentsA 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 midsegmentsA 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 additionA 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 additionMuch like triangles, the midsegment is parallel to the sides it does not touch.

So find its length?So find its length?Add the bases and divide by 2.Working backwardsWorking backwardsFormula:Working backwardsPlug in the length of the midsegment.Plug in the length of a base.Solve for the remaining baseSolve for the remaining baseOr

Solve for the remaining baseOrArithmetically, multiply the length of the midsegment by 2 and subtract the length of the given base.

Heres a problem I enjoy.Given an isosceles trapezoid whose midsegment measures 50 cm and whose legs measures 24 mm. Find its perimeter.Now to kites:

If we drew in a line of symmetry, where would it be?

And now are there s?

KEY TEY

What new is congruent by CPCTC?

These are called the non-vertex angles, because they connect the non congruent sides

What else is congruent by CPCTC

What else is congruent by CPCTC?

The original angles, E and Y, are the vertex angles, and we can conclude they are bisected by the diagonal.

The original angles, E and Y, are the vertex angles, and we can conclude they are bisected by the diagonal.

The vertex angles of a kite are the common endpoints of the congruent sides.SummarizingSummarizingVertex angles connect the congruent sides and are bisected by the diagonals.SummarizingVertex angles connect the congruent sides and are bisected by the diagonals.Non vertex angles connect the non-congruent sides and are congruent.One last property that becomes Theorem 6-22

If we draw in both diagonals

If a quadrilateral is a kite, then its diagonals are perpendicular.

Problem solving examples

Which group breaks down more?

Which group breaks down more?

Which group breaks down more?

And if we combine the last 2?

And if we combine the last 2?

And if we combine the last 2?

Those are all the definitionsThose are all the definitionsYou need to remember all the properties, especially the ones that work for parallelograms, since they also work for a rhombus, rectangle, and square.In additionYou need to remember all the properties, especially the ones that work for parallelograms, since they also work for a rhombus, rectangle, and square.In additionYou need to determine the truth value (true/false) of a universal statementIn additionYou need to determine the truth value (true/false) of a universal statement

All rectangles are parallelograms.In additionYou need to determine the truth value (true/false) of a universal statement

All rhombi are squares.