Scale Factor
Similar Polygons
Are the figures similar?
More Scale Factor
More Scale Factor
100
Find the Scale Factor
4/3
100
The polygons are similar. Find the value of x.
x = 12
100
Determine whether the triangles are similar. If they are, write a similarity statement. SHOW WORK.
no; m∠R = 60° and m∠V=80; corresponding angles are not congruent.
100
The coordinates below represent a triangle that was dilated.
J(-3, -12) to J’(-2, -8)
K(-6, -15) to K’(-4, -10)
L(-9, -12) to L’(-6, -8)
What was the scale factor that was used in the dilation?
2/3
100
(NOT ON THE TEST )Triangle AEB is simiar to Triangle ADC. Find AB
AB = 21
200
Find the Scale Factor.
1/3
200
The polygons are similar. Find the value of x.
x = 11
200
Determine whether the triangles are similar. If they are, write a similarity statement. SHOW WORK.
yes; ∠H ≅ ∠J and ∠F ≅ ∠K, so △FGH ∼ △KLJ,
corresponding angles are congruent.
200
True or False?
A dilation always enlarges a figure
False
200
True or False:
A dilation will always produce similar figures
True
300
Find the scale factor.
3/4 or 0.75
300
The polygons are similar. Find the values of x and y.
x = 7.5, y = 166
300
Are the two triangles are similar.
∠N ≅ ∠Z and ∠MYN ≅ ∠XYZ (vertical angles), and by default m and x are congruent since all angles of a triangle add to 180, so △MYN ∼ △XYZ.
300
Verify that △ABC ∼ △DEF. Find the scale factor of △ABC to △DEF.
△ABC: BC = 18, AB = 15, AC = 12
△DEF: EF = 12, DE = 10, DF = 8
300
Does the algebraic representation show an enlargement or a reduction?
(6/5 x, 6/5 y)
enlargement
400
(This is not on the test) The polygons are similar. The area of one polygon is given. Find the area of the other polygon.
Area = 90 square cm
400
The polygons are similar. Find the values of x and y.
x = 35.25, y = 20.25
400
Are that the two triangles are similar. Angles L and NMP are both 30 degrees.
∠N ≅ ∠N, because they are the same angle, and by default, because the sum of the angles of a triangle add to 180 then ∠Q ≅ ∠MPN, so △LNQ ∼ △MNP.
400
True or False:
A dilation will always change the orientation of a figure.
False
400
Dilate the figure with a scale factor of 2.5.
A(4, 3)
B (5, 7)
C(9, 12)
A' (10, 7.5)
B' (12.5, 17.5)
C'(22.5, 30)
500
The polygons are similar. The area of one polygon is given. Find the area of the other polygon.
108 Square Feet
500
In table tennis, the table is a rectangle 9 feet long and 5 feet wide. A tennis court is a rectangle 78 feet long and 36 feet wide. Are the two surfaces similar? Explain. If so, find the scale factor of the tennis court to the table.
no; Corresponding side lengths are not proportional.
500
(this is not on the test) A flagpole casts a shadow that is 50 feet long. At the same time, a woman standing nearby who is 5 feet 4 inches tall casts a shadow that is 40 inches long. How tall is the flagpole to the nearest foot? (Two similar triangles are formed when you draw the picture)
You can use a proportion to fi nd the height x. Write 5 feet 4 inches as 64 inches so that you can form two ratios of feet to inches.
x ft / 64 in. = 50 ft / 40 in.
Write proportion of side lengths.
40x = 3200 Cross Products Property
x = 80 Solve for x.
The flagpole is 80 feet tall.
500
Certain sections of stained glass are sold in triangular pieces. Which of the three pieces, if any, are similar?
The pieces with side lengths of 5.25 inches and 7 inches (red and turquoise)
500
If the scale factor is 4:
The perimeter of the first triangle is 8. What is the perimeter of the next triangle?
If the area of the first triangle is 8, what is the area of the 2nd triangle?
Perimeter = 32
Area = 64