Test PracticeT
298 Proportions and Similarity
- SHORT RESPONSE Triangles ABC and
DEF shown below represent 2 puzzle
pieces. Triangle ABC is similar to triangle
DEF.
"
$ #
%
5 cm & '
2 cm
8 cm
Ycm
What is the length of
−−
EF?
- GRIDDED RESPONSE Horatio is 6 feet
tall and casts a shadow 3 feet long. What
is the height in feet of a nearby tower if
it casts a shadow 25 feet long at the
same time?
3 ft
h ft
6 ft
25 ft Not to scale
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AboutAbout
Two triangles are similar if their corresponding sides are proportional. This is called
Side-Side-Side Similarity (SSS). They are also similar if their corresponding angles are
congruent. This is called Angle-Angle Similarity (AA).
Are there any other ways to test for similarity? Try the following activity.
Draw a 30° angle that is formed by a segment
30 °
3 cm
5 cm
measuring 3 centimeters and a segment
measuring 5 centimeters.
Draw a 30° angle that is formed by a segment
30 °
4.5 cm
7.5 cm
measuring 4.5 centimeters and a segment
measuring 7.5 centimeters.
Form two triangles by connecting the endpoints of both pairs of segments.
Measure the lengths of the formed segments.
Show that corresponding sides are proportional.
- Are the two triangles similar? Justify your response.
Repeat Steps 1–3 using the following angle and segment measurements.
- 60°; 1 inch, 1.5 inches 19. 45°; 3 inches, 5 inches
60°; 2 inches, 3 inches 45°; 9 inches, 15 inches - Are the triangles similar? Justify your response.
- MAKE A CONJECTURE The activities suggest another way to test triangles for
similarity. This is called Side-Angle-Side Similarity (SAS). Write a sentence
or two that explains Side-Angle-Side Similarity.
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