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Use Properties of Trapezoids and Kites

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## Use Properties of Trapezoids and Kites

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**Use Properties of Trapezoids and Kites**Chapter 8.5**Trapezoids**• Trapezoids are quadrilaterals that have 2 parallel sides • The parallel sides are called the bases. • A trapezoid has 1 pair of base angles. • The non-parallel sides are called the legs. base Leg Leg base**Is it a trapezoid?**Are the bases parallel? Find the slope of each base. If the slopes are the same, then it is a trapezoid.**Isosceles Trapezoids**• Isosceles triangles have 2 congruent sides with 2 pairs of congruent angles. • The diagonals of an isosceles trapezoid are also congruent.**If it is Isosceles find the missing angles.**It is isosceles! 53º 127º 127º Because it is an isosceles trapezoid, the base angles are congruent. Therefore m <A = m <B, and m <D = m <C Angle A and Angle D are supplementary. 180 – 53 = 127**Find the missing angles if it is an Isosceles Trapezoid.**83º 97º 83º**Midsegments**• A midsegment is a segment that connects 2 midpoints. • The midsegment of a trapezoid connects the midpoints of the legs.**Things always have to be more difficult**19.5 5x + 3**Find x**45 52.5 10x + 15**Kites**• A kite is a quadrilateral with 2 pairs of congruent sides, but the opposite sides are not congruent.**Diagonals**If the diagonals of a kite are perpendicular, then what shape is created by the diagonals? If we are given these side lengths, can we find the missing sides XY, WX, YZ , and WZ?**Find XY, ZY, WX, and WZ**2√13 6√5**Find XY, YZ, WZ, and WX**5√5 √461**The figure below is a kite, find the missing angles**What is the sum of the interior angles of a kite? 360 100 + 40 + mó E + mó G = 360 140 + mó E + mó G = 360 mó E + mó G = 220 What do we know about the measures of the angles E and G? They are congruent!**Find the missing angles**What do we know about the measures of the angles F and H? They are congruent! 110º 60 + 110 + 110 + mó G = 360 80º 280 + mó G = 360 mó G = 80**Find the missing angles**150 + 90 + mó F + mó G = 360 240 + mó F + mó G = 360 mó F + mó G = 120 mó F = mó G