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Trapezoids and Kites Geometry 6-5
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Recall the shape of a toy kite
Recall the shape of a toy kite. What definition would you write to describe the shape in geometric terms? Kite Investigation
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Kite Investigation Kite Definition
A kite is a quadrilateral that has two pairs of consecutive congruent sides, but the opposite sides are not congruent Kite Investigation
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Get your supplies Straight Edge Patty Paper Kite Investigation
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On a piece of patty paper, draw two line segments of different length
Kite Investigation
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Fold the paper, so that the endpoints are exactly on the fold
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Trace the first two segments through the patty paper
Kite Investigation
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Kite Investigation Unfold the paper and label your kite G,L,A,D L G A
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Kite Investigation Measure each of the four angles
What conclusions can you draw? L G A D Kite Investigation
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Kite Angles Conjecture
The non-vertex angles of a kite are congruent Kite Angles Conjecture
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Kite Investigation Add the diagonals into your diagram
Label the intersecting point M L G M A D Kite Investigation
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Kite Investigation Measure the angles at point M
What can you conclude about the diagonals? L G M A D Kite Investigation
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Kite Diagonals Conjecture
The diagonals of a kite are perpendicular Kite Diagonals Conjecture
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Measure LM and MD What can you conclude? L G M A D Kite Investigation
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Kite Diagonal Bisector Conjecture
The diagonal connecting the vertex angles of a kite is the perpendicular bisector of the other diagonal Kite Diagonal Bisector Conjecture
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Kite Investigation Fold along the diagonals
Does either diagonal bisect any angles? L G M A D Kite Investigation
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Kite Angle Bisector Theorem
The vertex angles of a kite are bisected by a diagonal Kite Angle Bisector Theorem
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Schedule Quiz on Tuesday / Wednesday 4 questions Classifying
Parallelograms Proving Parallelograms Rhombus / Rectangle / Square Schedule
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Trapezoid Definition Trapezoid Definition
A trapezoid is a quadrilateral with exactly one pair of parallel sides Trapezoid Definition
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Trapezoid Vocabulary Trapezoid Definitions
The parallel sides are called bases A pair of angles that share a base are called base angles A&B, C&D A B C D Trapezoid Vocabulary
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Trapezoid Consecutive Angles Theorem
The consecutive angles between the bases of a trapezoid are supplementary Trapezoid Consecutive Angles Theorem
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Trapezoid Investigation
Isosceles Trapezoid An isosceles trapezoid has congruent legs A B C D Trapezoid Investigation
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Trapezoid Investigation
Get your supplies Protractor Straight Edge - Ruler Paper Compass Trapezoid Investigation
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Trapezoid Investigation
Draw two parallel lines – at least two inches apart Use a compass to create two equal length legs Label the vertices L,I,O,N L I O N Trapezoid Investigation
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Trapezoid Investigation
Measure each pair of base angles angle L = ? angle I = ? angle O= ? angle N = ? L I O N Trapezoid Investigation
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Trapezoid Investigation
What can you conclude about the base angles in an isosceles trapezoid? L I O N Trapezoid Investigation
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Isosceles Trapezoid Theorem
The base angles of an isosceles trapezoid are congruent Isosceles Trapezoid Theorem
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Trapezoid Investigation
Add the diagonals of the isosceles trapezoid L I O N Trapezoid Investigation
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Trapezoid Investigation
Compare the lengths of the two diagonals What conclusion can we make? L I O N Trapezoid Investigation
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Isosceles Trapezoid Diagonals Theorem
The diagonals of an isosceles trapezoid are congruent Isosceles Trapezoid Diagonals Theorem
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Practice Problems
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53° 127° 127° Practice Problems
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DF=10 Angle C=85° Angle D=95° Angle F=85° Practice Problems
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a = 129.5° h = 129.5° Practice Problems
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a = 118° t = 43° Practice Problems
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90° 48° Practice Problems
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Pages 322 – 325 2-16 even, 22-24, 27,28,32-37, 56 Homework
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