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Daily Check Refer to parallelogram GHOST to answer the following.
Solve for x. Find If HT = 32, find HS. G H O S T 42 28 5x + 2 4(x + 2)
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Review Problems 8/27/12 In , is 34 and is 58. What is the longest side of the triangle? 2. What is the measure of EACH interior and exterior angle of a regular convex a) octagon? b) dodecagon? c) 20-gon? 3.Given the following angles measurements for a polygon, find the number of sides. a) Each exterior angle of a regular polygon is 40°. b) Each exterior angle of a regular polygon is 20°. c) The sum of the interior angles of a polygon is 1800°. d) The sum of the interior angles of a polygon is 1080°.
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Homework Review 7) Rhombus, square 8) Rectangle, Square
9) Parallelogram, Rhombus 10) Rectangle, Square 11) Rectangle, Square 12) Rhombus, Square 13) All ) Square 15) Square; x = 2, y = 1 16) Rhombus; x = 27, y = 4 17) 30° 18) 90° 19) 12 21) 40° 22) 100° 23) 6 25) 90° 26) 45° 27) ) 5√2
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EOCT Practice Question of the Day
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What special properties apply to trapezoids and kites?
GPS Geometry Day 11 ( ) UNIT QUESTION: What are the properties and characteristics of polygons? Standard: MM1G1.e. Today’s Question: What special properties apply to trapezoids and kites? Standard: MM1G.1.e.
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Trapezoids and Kites
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EQ: What are the characteristics of a trapezoid?
Trapezoids EQ: What are the characteristics of a trapezoid?
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Have only one pair of opposite sides that are parallel.
Trapezoids Have only one pair of opposite sides that are parallel. base leg
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If the legs are congruent then the trapezoid is an
Isosceles Trapezoid
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Isosceles Trapezoids have TWO other special properties
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Each pair of base angles is congruent
Isosceles Trapezoid Each pair of base angles is congruent
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Diagonals are congruent
Isosceles Trapezoid Diagonals are congruent
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Example 1 Find the other angles in this isosceles trapezoid.
B
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Side note: ALL Trapezoids Have a Median
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The MEDIAN connects the midpoints of the legs
B A C D E F The MEDIAN connects the midpoints of the legs
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its length is half the sum of the bases
Median Theorem for Trapezoids The median is: parallel to each base and its length is half the sum of the bases
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Which means…
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Example 2 Find the length of the median MN in trapezoid ABCD if AB = 20 and CD = 16.
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EXAMPLE 3 EF is the median of trapezoid ABCD. Find EF. 22 in. A B EF = 16 E F C D 10 in.
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EXAMPLE 4 BC is the median of trapezoid MATH. Find MA. MA = 8 15 in.
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EXAMPLE 5 BC is the median of trapezoid TRAP. Find TR. TR = 27 T R 19 in. B C P 11 in. A
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4 Properties of Kites
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No sides have to be parallel
KITES No sides have to be parallel
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ONE diagonal is the perpendicular bisector to the other
KITES ONE diagonal is the perpendicular bisector to the other
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KITES TWO pairs of consecutive congruent sides, but opposite sides are NOT congruent. (Recall the equidistant theorem)
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Only ONE pair of opposite angles are congruent
KITES Only ONE pair of opposite angles are congruent
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KITES B Example 1: 83° A 41° C D Find the measure of D. 118°
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KITES K Example 2: 6 15 J L 8 M Find JK and KL.
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Homework p. 325 #3-14
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