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Mr. Wolf
Tuesday 11/11/08
Geometry
Grades 10-12
Unit 6: Similarity
Similar Polygons
Materials and Resources:
 Ratio Riddles Warm-up (1 per student)
 Similar Polygons Notes (1 per student)
 Similar Polygons Drawing Activity sheet (1 per student)
 Rulers, protractors (1 pair per student)
 Exit Ticket (1 per student)
PA Standards Addressed:
2.1.8 D. Apply ratio and proportion to mathematical problem situations involving
distance, rate, time and similar triangles.
Instructional Objectives:
 Students will be able to define similar and identify figures that are similar.
 Students will be able to calculate side lengths, angle measures, and scale factors
of similar polygons.
Time
10 min
1 min
1 min
15 min
Activity
Warm-up
Agenda
Homework Check
Review Homework
min
Similar Polygons
Notes
min
Similar Polygons
Drawing Activity
Description
Pass out the Warm-up and review solutions.
Review the goals for the day.
Spot-check and review solutions
Present the HW solutions and answer any
questions.
Modeling: Pass out the notes sheets and provide
students with information.
Guiding: Help students complete example
problems.
Independent Practice: Students will complete the
problems on the back of the sheet.
Assessment: Review solutions.
Modifications:
Students with special needs will be given figures to
illustrate the problems on the back.
Advanced students will be called on when
reviewing solutions.
Modeling: Pass out the instructions, rulers, and
protractors.
Guiding: Help students complete the sheet.
Independent Practice: Students will draw the four
figures and calculate dimensions.
Assessment: Sheets will be collected and graded.
1 min
5 min
Agenda
Conclusion
Homework:
Pg. 251 #15, 17-21, 24-27
Lesson Reflection:
Modifications:
Students with special needs will be given one figure
and will need only draw the similar figure.
Advanced students will be given more challenging
dimensions and scale factors.
Revisit goals and identify whether they were met.
Pass out the Exit Ticket and collect at the bell.
Geometry Fall 2008
Name: ________________________
Ratio Riddles Warm-up
1) Find the measures of two complementary angles whose ratio is 4:5.
2) Find the measures of two supplementary angles whose ratio is 11:4.
3) Find the measures of the angles in a triangle whose ratio is 3:4:5.
4) Find the measures of the acute angles of a right triangle whose ratio is 5:7.
5) Find the measures of the angles in an isosceles triangle whose ratio is 3:3:2.
6) Find the measures of the angles in a hexagon whose ratio is 4:5:5:8:9:9.
7) The perimeter of a triangle is 132cm and the lengths of its sides are in the ratio
8:11:14. Find the length of each side.
8) What is the ratio of the measure of an interior angle to the measure of an exterior
angle in a regular hexagon?
Geometry Fall 2008
Name: ________________________
Ratio Riddles Warm-up
1) Find the measures of two complementary angles whose ratio is 4:5.
2) Find the measures of two supplementary angles whose ratio is 11:4.
3) Find the measures of the angles in a triangle whose ratio is 3:4:5.
4) Find the measures of the acute angles of a right triangle whose ratio is 5:7.
5) Find the measures of the angles in an isosceles triangle whose ratio is 3:3:2.
6) Find the measures of the angles in a hexagon whose ratio is 4:5:5:8:9:9.
7) The perimeter of a triangle is 132cm and the lengths of its sides are in the ratio
8:11:14. Find the length of each side.
8) What is the ratio of the measure of an interior angle to the measure of an exterior
angle in a regular hexagon?
Geometry Fall 2008
Name: ________________________
Similar Polygons Notes
Two polygons are similar if…
Example: Polygon PQRST is similar to polygon UVWXY
Notation:
Because the polygons are similar, the following statements are true:
If two polygons are similar, then the ratio of the lengths of two corresponding sides is
called the scale factor of the similarity.
Example: Given ABC ~ DEF .
Calculate the scale factor of the similarity.
Use the scale factor to find the values of x and y.
Practice Problems:
Determine whether the following figures are similar always, sometimes, or never.
1) Two equilateral triangles.
_______________
2) Two isosceles triangles.
_______________
3) Two squares.
_______________
4) Two regular polygons.
_______________
5) An isosceles triangle and a scalene triangle.
_______________
6) Two rhombuses.
_______________
7) A right triangle and a scalene triangle.
_______________
8) Two isosceles triangles.
_______________
9) Two rectangles.
_______________
10) Two regular hexagons.
_______________
Given: quadrilateral MATH ~ quadrilateral M’A’T’H’
mY ' _______
mD  _______
The scale factor of quadrilateral MATH to quadrilateral M’A’T’H’ is ________.
TH  _______
M ' A'  _______
M ' H '  _______ (in terms of t)
The ratio of the perimeters is ___________
Explain why it is not true that quadrilateral THMA ~ quadrilateral A’M’H’T’.
Geometry Fall 2008
Name: ________________________
Similar Polygons Drawing Activity
Materials:
 Ruler
 Protractor
 Pencil
Goal:
To construct similar polygons using various scale factors.
Figure 1:
1) Draw quadrilateral JKL M with the following dimensions:
J  80
K  65
L  137
JK  12cm
KL  5cm
LM  9cm
M  78
MJ  8cm
2) Draw quadrilateral NOPQ so that quadrilateral JKLM ~ quadrilateral NOPQ
by a scale factor of 2:3.
3) Calculate the following dimensions of quadrilateral NOPQ .
N  ________
O  ________
P  ________
Q  ________
NO  ________
OP  ________
PQ  ________
QN  ________
Figure 2:
1) Draw ABC with the following dimensions:
B  24
A  50
AB  14cm
C  106
BC  11cm
AC  6cm
2) Draw DEF so that ABC ~ DEF by a scale factor of 2:1.
3) Calculate the following dimensions of DEF .
D  ________
E  ________
F  ________
DE  ________
EF  ________
DF  ________
Geometry Fall 2008
Name: ________________________
Exit Ticket
Given polygon ABCDE ~ polygon FGHJK by a scale factor of 3:1. Find the following
lengths.
CD  ________
AE  ________
Geometry Fall 2008
FG  ________
GH  ________
Name: ________________________
Exit Ticket
Given polygon ABCDE ~ polygon FGHJK by a scale factor of 3:1. Find the following
lengths.
CD  ________
AE  ________
FG  ________
GH  ________