Download 6.1

Chapter 6
Similarity of Figures
6.1 – Similar Polygons
6.2 – Determining if two Polygons are Similar
6.3 – Drawing Similar Polygons
6.4 – Similar Triangles
21 Name: ____________________________________
Math 10 Workplace
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Math 10 Workplace
Marsh
6.1 – Similar Polygons
A. What makes something similar to something else?
Two figures are similar if they have the _________________________, (angles and
proportion of sides) but are __________________________. What are some examples
of things that are similar?
Examples: photographs can be enlarged or reduced; scale models of buildings
Rules: for two figures to be similar they have to have the __________________ and
the ___________________ sides must be the same proportion.
Recall: Proportions from chapter 1:
_______________ is when you state that two fractions are equal.


Solve for :
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For two figures to be similar:
 _____________________________ must be the same size; and

_____________________________ must be in the same proportion
In quadrilateral ABCD and quadrilateral WXYZ, the following equivalencies are true:
A = W
B = X
C = Y
D = Z
AB BC YZ
DA



WX XY DC ZW
These two quadrilaterals are similar. This can be written as: ABCD ~ WXYZ.
Worksheet: Similar Figures
Similar Figures Worksheet
1) Trapezoid DEFG is similar to trapezoid JKLM, as shown below. State the
corresponding sides and angles.
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2) Identify the pairs of similar polygons below by letter names. Use the grid to
determine lengths. Explain your reasoning.
B. Determining Sides in Similar Figures
When working with the length of sides in similar figures, the figures being either a
____________________ or an ______________________ of each other, the ratio of
the corresponding sides is always the ____________. What this means is that by using
a proportion, you can determine the lengths of all the unknown sides in both figures.
You can determine the _____________________ of the figures.
Example 1:
The two figures below are similar. Find the lengths of the side of the smaller figure.
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Example 2:
Tara has drawn a scale diagram of her bedroom so that she can sketch different
arrangements of her furniture. On her diagram, the walls have the following lengths:
If the longest wall in her room is actually 12.75ʹ, how long are the other walls?
Worksheet: Determining Sides in Similar Figures
Math 10 Workplace
Marsh
Determining Sides in Similar Figures Worksheet
1) The two figures shown below are similar. Find the lengths of the sides of the
smaller figure. (The diagrams are not drawn to scale.)
2) On a blueprint, a room measures 2.75 inches by 1.5 inches. If 1 inch represents 8
feet, what will be the dimensions of the room?
3) Jason wants to build a model of his house. He will build the model using a scale
where 5 cm represents 2 m. If one room is 6.5 m long, 4.8 m wide, and 2.8 m tall,
what will its dimensions be in the model?
4) If a house is 40 feet long, 35 feet wide, and the top of the roof is 27 feet above
ground level, what will the corresponding dimensions be of a model built so that 1
foot is represented by ½ inch?
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5) Michaela has a microscope that enlarges images between 40 and 1600 times.
How large will an object that is 1.2 mm by 0.5 mm appear to be at each of these
extremes?
6) The scale of a model airplane to the actual airplane is 2:45. If the model is 38
centimetres long, how long is the actual airplane?
7) Theresa folds origami paper to make stacked boxes. The outer box is 12 cm by 8
cm by 4 cm. Theresa would like to make three smaller, similar boxes, each scaled
down by ¼ of the previous box. What are the dimensions of the three smaller
boxes?
Answers:
1) LP = 7 cm; OP = 6 cm; ON = 4 cm; MN = 6 cm 2) 22 ft by 12 ft 3) 16.25 cm, 12 cm, 7 cm 4) 13.5”,
17.5”, 20” 5) 48 by 20; 1920 by 800 6) 855 cm 7) box1: 3, 6, 9; box 2 = 2.25, 4.5, 6.75; b0x 3 =
1.69, 3.38, 5.06
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C. Similar Triangles
Since corresponding angles in similar figures must be equal, the only difficulty with
determining the angle measures is making sure that the figures are arranged so they
look the ________________. Sometimes this will already be done for you. But other
times, you must carefully look at this arrangement.
Example 3:
If ∆RST is similar to ΔLMN and angle measures of ΔLMN are as follows, what are the
angles measures of ∆RST?
Example 4:
Two triangles are similar. One has sides of 8 m, 5 m, and 6 m. If the longest side of the
second triangle is 5 m, what are the lengths of the other two sides?
Worksheet: Similar Triangles
Math 10 Workplace
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Similar Triangles Worksheet
1) If ΔABC is similar to ΔXYZ and the following angle measures are known, what
are the values of the remaining angles?
2) If two polygons ABCDEF and GHIJKL are similar, and the following angle
measures are given, state the corresponding angles and their measures.
3) If trapezoid PQRS is similar to trapezoid LMNO, what are the values of w, x, y,
and z?
4) A pentagon has interior angles of 108°, 204°, 63°, 120°, and 45°. Rudy wants to
draw a similar pentagon with sides twice as long as the original. What size will
the angles be?
Answers:
1) A=X=32°,C Z 48°,Y B 100°2) J=D=73°;B H 21°;K E 40°
3 w 42°,x 45cm,y 70°,z 17.5cm4 108°, 204°, 63°, 120°, and 45°
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