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LC Math 2 Adv – Similar Figures (LT 6 & 7)
1. Determine if the figures in the diagram to the
right are similar by utilizing similarity
transformations. Specify those transformations
below and write the appropriate similarity
statement. (hint: point F has been included to
be part of a specific transformation!)
2. Jane claims that the two figures in the diagram are similar because she measured the sides and angles. However,
she left her work at home! Show the work necessary to support her claim below and see if you reach the same
conclusion.
⃗⃗⃗⃗⃗ and 𝑂𝑃′ = 𝑘 ∙ 𝑂𝑃. With this in mind,
3. Recall: if a figure is dilated about point O, the image of point P will lie on 𝑂𝑃
how can you calculate the scale factor, given two similar figures? Explain.
4. Are the triangles in the diagram to the right similar? Show/explain
how you know.
5. The accompanying diagram shows two similar triangles.
Which proportion could be used to solve for x?
1)
𝑥
9
24
= 15
2) 24 9
=
15 𝑥
𝑥
3) 32
=
12 15
4) 32 12
=
15
𝑥
Explain your choice.
6. Use a protractor and a ruler to measure the angles and side lengths and determine if Quadrilateral ABCD ~
Quadrilateral A’B’C’D’. Then fill in the table below.
Side Lengths
(use mm)
a. Are the measures of the corresponding angles equal?
b. Are the ratios of the corresponding side lengths equal?
Angle Measures
𝐴𝐵 =
𝐴′ 𝐵′ =
𝑚∠𝐴 =
𝑚∠𝐴′ =
𝐵𝐶 =
𝐵′ 𝐶 ′ =
𝑚∠𝐵 =
𝑚∠𝐵′ =
𝐶𝐷 =
𝐶 ′𝐷′ =
𝑚∠𝐶 =
𝑚∠𝐶 ′ =
𝐴𝐷 =
𝐴′ 𝐷 ′ =
𝑚∠𝐷 =
𝑚∠𝐷′ =
c. Are the figures similar? Explain.
7. Rebecca says that if two triangles are congruent, then they must be similar. Leon disagrees. He says that pairs of
triangles can be congruent or similar but not both. What do you think? Explain your reasoning.
8. Draw a quadrilateral that is similar (but not congruent) to the one given below. Measure and
label all sides and angles of quadrilaterals 𝑀𝐴𝑇𝐻 and 𝑀′𝐴′𝑇′𝐻′. Write a similarity statement.
9. The large rectangle shown is a golden rectangle. This means that when a square is cut off, the rectangle that
remains is similar to the original rectangle.
a) How wide is the original rectangle? Round your answer to the nearest tenth.
x
x
6
b) The ratio of length to width in a golden rectangle is called the golden ratio. Write the golden ratio in simplified
radical form. Then use a calculator to find an approximation to the nearest hundredth.