7th Grade Math

Test PracticeT

298 Proportions and Similarity

15. 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

Y
cm

What is the length of

−−

EF?

16. 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

Similar Figures

More

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.

17. Are the two triangles similar? Justify your response.

Repeat Steps 1–3 using the following angle and segment measurements.

18. 60°; 1 inch, 1.5 inches 19. 45°; 3 inches, 5 inches
    60°; 2 inches, 3 inches 45°; 9 inches, 15 inches


19. Are the triangles similar? Justify your response.


20. 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.

293_303_C05_L3_895130.indd 298 12/29/09 1:10 PM