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Geometry Polygons Lesson 8-6: Applications of polygons Objectives: Students will be able to apply the skills and knowledge from definitions and theorems about polygons/quadrilaterals to a variety problems and proofs. Procedure: HW discussion Quiz: parallelogram proof Do Now Animoto: http://animoto.com/play/RfUcVFIA2c9fcwtPVb3a1Q#embed Proof practice Polygon Jeopardy (also in my math links) –white boards http://www.salem.k12.va.us/staff/bmoody/polygonjeopardy.ppt Homework: Parallelogram proofs WS 8-6 Portfolio 8 Test next class!! Name:___________________________ Lesson 8-6 Applications Find the area of math. Blast from the past: 1) The sides of a triangle are 8, 15 and 18. Find the length of the longest side of a similar triangle whose shortest side is 19. 2) If the lengths of 2 similar cubes are in a ratio of 4:9, what is the ratio of each of the following: a) their volumes?_____ c) their surface areas?____ b) the diagonals of the faces?_____ 3) In ∆ ABC, find x given that DE||AB, CE = 3, BE = x, CD = x + 1, & AD = x + 5. B E A D 4) In ∆ ABC, find x given that DE||BC, AD = 3, DE= 4 and DB = 6, find BC. 5) C Name:__________________________ Geometry 8-6 Mixed practice proofs 1) Given: ABCD is a parallelogram. AE CF Prove: EOB FOD Statements 1) ABCD is a parallelogram. AE Reasons CF 1) given 2) Given: Trapezoid ABCD with AB || DC Prove: (AE)(DE) = (CE)(BE) Statements 1) Trapezoid ABCD with AB || DC Reasons 1) Given 3) Statements 1) Reasons 1) Given 4) a) Prove: EM || TB Statements 1) Reasons 1) Given b) If given: ED HT ; MH DB; MHT EDB How would this change your proof? Hints for proof #1: Parallelograms have opposite sides that are congruent. You need to use PSS to get the sides of the triangles congruent Parallelograms have opposite sides that are parallel. Use parallel line theorem once or twice (ASA) May use vertical angles (AAS) Hints for proof #2: Prove similar triangles (AA) Use parallel line theorem Work backwards to get the proportion Last 2 reasons: Corresponding sides of similar triangles are in proportion. In a proportion, the product of the means equals the product of extremes. Hints for proof #3: Rhombuses have 4 congruent sides Use substitution Think about the isosceles triangle theorem Hints for proof #4: Get congruent triangles by using RAPS Use cpctc on alternate interior angles Use theorem to prove parallel lines Part b- you would need to state there are supplementary angles and supplements of congruent angles are congruent. Name:_____________________________________ Geometry HWS 8-6 mixed practice You need to complete these problems and then check the key on my website! Write your one page reflective portfolio 8 (use the outline on the website) 1) Which statements describe the properties of a rhombus? a. The diagonals are perpendicular. b. The diagonals are congruent. c. The diagonals bisect each other. d. The diagonals bisect the angles Choose: 1) a,b,c and d 2) a,c and d 3) a and c 4) b and d 2) The diagonals of a rhombus are 10 and 24. Find the perimeter of the rhombus. 3) The measures of angles A and B of parallelogram ABCD are in the ratio of 3 :7. Find the measure of the larger angle. 4) EF is the median (mid-segment) of trapezoid ABCD. BC = 2x - 8 and AD = 3x + 5 EF = 16. Find BC. 5) If the area of a trapezoid is 348 sq. units and the bases are 22 and 36 units long, find the height. 6) a) If AE = 10 and BD = 26, find the area of ABCD. b) If AC= 40 and BE = 30, find AB. 7) What is the value of x? 8) 9) What is the total number of diagonals of a nonagon? 10) What is the sum of the measures of the interior angles of a dodecagon? 11) What is the number of sides of a polygon if the sum of the measures of the interior angles is 1260˚? 12) Find the measure of each interior angle of a regular octagon. 13) What is the number of sides of a polygon if each exterior angle measure 18˚? Did you check your answers on my website? Did you make your portfolio? Test is next block!!!!