Download Unit 8

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!!!!