Trapezoids and Kites Geometry 6-5

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

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

Get your supplies Straight Edge Patty Paper Kite Investigation

On a piece of patty paper, draw two line segments of different length Kite Investigation

Fold the paper, so that the endpoints are exactly on the fold Kite Investigation

Trace the first two segments through the patty paper Kite Investigation

Kite Investigation Unfold the paper and label your kite G,L,A,D L G A

Kite Investigation Measure each of the four angles What conclusions can you draw? L G A D Kite Investigation

Kite Angles Conjecture The non-vertex angles of a kite are congruent Kite Angles Conjecture

Kite Investigation Add the diagonals into your diagram Label the intersecting point M L G M A D Kite Investigation

Kite Investigation Measure the angles at point M What can you conclude about the diagonals? L G M A D Kite Investigation

Kite Diagonals Conjecture The diagonals of a kite are perpendicular Kite Diagonals Conjecture

Measure LM and MD What can you conclude? L G M A D Kite Investigation

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

Kite Investigation Fold along the diagonals Does either diagonal bisect any angles? L G M A D Kite Investigation

Kite Angle Bisector Theorem The vertex angles of a kite are bisected by a diagonal Kite Angle Bisector Theorem

Schedule Quiz on Tuesday / Wednesday 4 questions Classifying Parallelograms Proving Parallelograms Rhombus / Rectangle / Square Schedule

Trapezoid Definition Trapezoid Definition A trapezoid is a quadrilateral with exactly one pair of parallel sides Trapezoid Definition

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

Trapezoid Consecutive Angles Theorem The consecutive angles between the bases of a trapezoid are supplementary Trapezoid Consecutive Angles Theorem

Trapezoid Investigation Isosceles Trapezoid An isosceles trapezoid has congruent legs A B C D Trapezoid Investigation

Trapezoid Investigation Get your supplies Protractor Straight Edge - Ruler Paper Compass Trapezoid Investigation

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

Trapezoid Investigation Measure each pair of base angles angle L = ? angle I = ? angle O= ? angle N = ? L I O N Trapezoid Investigation

Trapezoid Investigation What can you conclude about the base angles in an isosceles trapezoid? L I O N Trapezoid Investigation

Isosceles Trapezoid Theorem The base angles of an isosceles trapezoid are congruent Isosceles Trapezoid Theorem

Trapezoid Investigation Add the diagonals of the isosceles trapezoid L I O N Trapezoid Investigation

Trapezoid Investigation Compare the lengths of the two diagonals What conclusion can we make? L I O N Trapezoid Investigation

Isosceles Trapezoid Diagonals Theorem The diagonals of an isosceles trapezoid are congruent Isosceles Trapezoid Diagonals Theorem

Practice Problems

53° 127° 127° Practice Problems

DF=10 Angle C=85° Angle D=95° Angle F=85° Practice Problems

a = 129.5° h = 129.5° Practice Problems

a = 118° t = 43° Practice Problems

90° 48° Practice Problems

Pages 322 – 325 2-16 even, 22-24, 27,28,32-37, 56 Homework