Math 128. Construction, Congruence, and Similarity
Similar Triangles and Similar Figures
T. Judson
Stephen F. Austin State University
Spring 2008
Learning Objectives1
• To understand and be able to apply the definition of similar geometric figures.
• To understand and be able to apply the Angle-Angle (AA) Property for similar triangles.
• To be able to separate a line segment into congruent parts using a straight edge and
compass.
Testing Your Knowledge
1. Which of the following figures are similar? Why?
(a) Any two equilateral triangles.
(e) Any two circles.
(b) Any two squares.
(f) Any two regular polygons.
(c) Any two rectangles.
(g) Any two regular polygons with the
same number of sides.
(d) Any two rhombuses.
2. Divide a line segment into 4 congruent parts using a straight edge and compass.
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Section 10.4 in R. Billstein, S Libeskind, and J. Lott. A Problem Solving Approach to Mathematics for
Elementary School Teachers, ninth edition. Addison Wesley, Boston, 2007
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3. Assume that the triangles in each of the figures below are similar. Find the measures
of the unknown sides.
4. Samantha want to know how far above the ground the top of a leaning flagpole is. At
high noon, when the sun is directly overhead, the shadow cast by the pole is 7 ft long.
Samantha holds a plumb bob with a string 3 ft long up to the flagpole and determines
that the point of the plumb bob touches the ground 13 inches from the base of the
flagpole. How far above the ground is the flagpole?
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