Chapter 6 Section 6.5B Kites and Trapezoids

Trapezoid ABCD with Bases USE PROPERTIES OF KITES AND TRAPEZOIDS Definition Trapezoid A B C D Trapezoid ABCD with Bases

Legs – Non-parallel sides Congruent legs make the trapezoid Isosceles USE PROPERTIES OF KITES AND TRAPEZOIDS Trapezoid Vocabulary Legs – Non-parallel sides Congruent legs make the trapezoid Isosceles A B C D Base Angles – Angle formed by a base and a leg Congruent base angles makes the trapezoid Isosceles

USE PROPERTIES OF KITES AND TRAPEZOIDS M L J K E B D F C A

Trapezoid ABCD is Isosceles USE PROPERTIES OF KITES AND TRAPEZOIDS Trapezoid ABCD is Isosceles mA = mB = x mD = mC = 112 mA + mB + mC + mD = 360 x + x +112 + 112 = 360 2x + 224 = 360 2x = 136 x = 68

A and D are Supplementary mA + mD = 180 mA + 90 = 180 mA = 90 USE PROPERTIES OF KITES AND TRAPEZOIDS A and D are Supplementary mA + mD = 180 mA + 90 = 180 mA = 90 B and C are Supplementary mB + mC = 180 132 + mC = 180 mC = 48

Trapezoid ABCD is Isosceles USE PROPERTIES OF KITES AND TRAPEZOIDS Trapezoid ABCD is Isosceles mA = mB = x mD = mC = 77 mA + mB + mC + mD = 360 x + x +77 + 77 = 360 2x + 154 = 360 2x = 206 x = 103

Trapezoid PQSR is Isosceles And Base Angles are  P  Q and R  S USE PROPERTIES OF KITES AND TRAPEZOIDS Theorem P Q R S Trapezoid PQSR is Isosceles And Base Angles are  P  Q and R  S

is a midsegment of Trapezoid ABCD A B USE PROPERTIES OF KITES AND TRAPEZOIDS Theorem is a midsegment of Trapezoid ABCD A B C D P Q

The length of the midsegment is equal to half the sum of the bases USE PROPERTIES OF KITES AND TRAPEZOIDS The length of the midsegment is equal to half the sum of the bases

The length of the midsegment is equal to half the sum of the bases USE PROPERTIES OF KITES AND TRAPEZOIDS The length of the midsegment is equal to half the sum of the bases

The length of the midsegment is equal to half the sum of the bases USE PROPERTIES OF KITES AND TRAPEZOIDS The length of the midsegment is equal to half the sum of the bases

USE PROPERTIES OF KITES AND TRAPEZOIDS Definition Kite Kite GHJK

USE PROPERTIES OF KITES AND TRAPEZOIDS Theorem Kite GHJK

USE PROPERTIES OF KITES AND TRAPEZOIDS Since the Diagonals are Perpendicular we can use the pythagorean theorem (MA)2 = 52 + 62 (AT)2 = 52 + 82 (MA)2 = 25 + 36 (AT)2 = 25 + 64 (MA)2 = 61 (AT)2 = 89

USE PROPERTIES OF KITES AND TRAPEZOIDS Theorem H  K Kite GHJK

One pair of Opposite angles are congruent USE PROPERTIES OF KITES AND TRAPEZOIDS mA = mH = x mT = 74, mM = 27 mA + mH + mM + mT = 360 x + x + 74 +27 = 360 2x + 101 = 360 2x = 259 One pair of Opposite angles are congruent

One pair of Opposite angles are congruent USE PROPERTIES OF KITES AND TRAPEZOIDS One pair of Opposite angles are congruent mA = mH = 118, mT = x mA + mH + mM + mT = 360 118 + 118 + 81 + x = 360 x + 317 = 360 x = 43

4. Definition Isosceles Trapezoid USE PROPERTIES OF KITES AND TRAPEZOIDS 3. Definition  ’s 4. Definition Isosceles Trapezoid

USE PROPERTIES OF KITES AND TRAPEZOIDS Quadrialteral with one pair of opp sides || and  base ’s is isosceles Trapezoid

HW #73 Pg 359-363 11-23 Odd, 29-41 Odd, 47, 49, 54-64 Even