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)

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°.

Homework Review 7) Rhombus, square 8) Rectangle, Square 9) Parallelogram, Rhombus 10) Rectangle, Square 11) Rectangle, Square 12) Rhombus, Square 13) All 4 14) 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 28) 5√2

EOCT Practice Question of the Day

What special properties apply to trapezoids and kites? GPS Geometry Day 11 (8-27-12) 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.

Trapezoids and Kites

EQ: What are the characteristics of a trapezoid? Trapezoids EQ: What are the characteristics of a trapezoid?

Have only one pair of opposite sides that are parallel. Trapezoids Have only one pair of opposite sides that are parallel. base leg

If the legs are congruent then the trapezoid is an Isosceles Trapezoid

Isosceles Trapezoids have TWO other special properties

Each pair of base angles is congruent Isosceles Trapezoid Each pair of base angles is congruent

Diagonals are congruent Isosceles Trapezoid Diagonals are congruent

Example 1 Find the other angles in this isosceles trapezoid. B

Side note: ALL Trapezoids Have a Median

The MEDIAN connects the midpoints of the legs B A C D E F The MEDIAN connects the midpoints of the legs

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

Which means…

Example 2 Find the length of the median MN in trapezoid ABCD if AB = 20 and CD = 16.

EXAMPLE 3 EF is the median of trapezoid ABCD. Find EF. 22 in. A B EF = 16 E F C D 10 in.

EXAMPLE 4 BC is the median of trapezoid MATH. Find MA. MA = 8 15 in.

EXAMPLE 5 BC is the median of trapezoid TRAP. Find TR. TR = 27 T R 19 in. B C P 11 in. A

4 Properties of Kites

No sides have to be parallel KITES No sides have to be parallel

ONE diagonal is the perpendicular bisector to the other KITES ONE diagonal is the perpendicular bisector to the other

KITES TWO pairs of consecutive congruent sides, but opposite sides are NOT congruent. (Recall the equidistant theorem)

Only ONE pair of opposite angles are congruent KITES Only ONE pair of opposite angles are congruent

KITES B Example 1: 83° A 41° C D Find the measure of D. 118°

KITES K Example 2: 6 15 J L 8 M Find JK and KL. 10 17

Homework p. 325 #3-14