Download Ch. 7 Review

Name__________________________________________________________Period_____________Date________________________ Chapter 7 Review 1. In the 2002 Major League baseball season, Sammy Sosa hit 49 home runs and was at bat 556 times. Find the ratio of home runs to the number of times he was at bat. 2. The sides of triangle are 3 inches, 4 inches, and 5 inches. Find the scale factor between the longest and shortest sides. 3. A doll house that is a 15 inches tall is a scale model of a real house with a height of 20 feet. What is the ratio of the height of the doll house to the height of the real house? 4. The ratio of the sides of a triangle is 8:15:17. If the perimeter of the triangle is 480 inches, find the length of each side of the triangle. 5. Solve each proportion. 3
9
2x + 3 5
x + 22 30
3 y
=
=
=
=
18.2
y
4 a.
b. 8
c. x + 2 10 d. 8 24 6. The ratio of the measures of the angles of a triangle is 5:7:8. Find the measure of each angle. 7. Match each description in the first column with a word or phrase from the second column. a. The ratio of two corresponding quantities i. Proportion r t
=
ii. Cross products b. r and u in the equation s u iii. Means c. a comparison of two quantities r t
iv. Scale factor =
d. ru and st in the equation s u v. Extremes e. an equation stating that two ratios are equal vi. Ratio r t
=
f. s and t in the equation s u 8. Each pair of polygons is similar. Find x and y. a. AC=8, BC=10, AB=x, DE=9, DF=12, EF=y b. AC=36, BC=40, AB=x, DE=18, DF=y, EF=30 9. A person 6 feet tall casts a 1.5 foot-­‐long shadow at the same time that a flagpole casts a 7 foot-­‐
long shadow. How tall is the flagpole? 10. Determine whether each statement is always, sometimes, or never true. a. Two similar triangles are congruent. b. Two equilateral triangles are congruent. c. Two rectangles are similar. d. Two acute triangles are similar. e. Two isosceles right triangles are congruent. f. Two right triangles are similar. 11. Complete each sentence. a. Two polygons that have exactly the same shape, but not necessarily the same size, are ___________________. b. Two polygons are congruent if their corresponding angles are _____________________and their corresponding sides are _______________________. c. If two polygons are similar with a scale factor of 1, then the polygons are ________________. d. Two polygons are similar if their corresponding angles are _______________________ and their corresponding sides are _______________________. e. In a proportion, the product of the _______________ equals the product of the _______________. 12. Determine whether each pair of triangles is similar. Justify your answer. a. AB ll DE b. c. d. 13. The heights of two vertical posts are 2 meters and 0.45 meter. When the shorter post casts a shadow that is 0.85 meter long, what is the length of the longer post’s shadow to the nearest hundredth? 14. Find the perimeter of the given triangle. a. ΔDEF, if ΔABC ∼ ΔDEF, AB=36, BC=20, CA=40, and DE=35. b. ΔXYZ, if ΔRST ∼ ΔXYZ, RS=20, ST=22, TR=24, and XY=10. 15. Find FG if ΔRST ∼ ΔEFG, SH is an altitude of ΔRST, FJ is an altitude of ΔEFG, ST=6, SH=5, and FJ=7. 16. Find MN if ΔABC ∼ ΔMNP, AD is an altitude of ΔABC, MQ is an altitude of ΔMNP, AB=24, AD=14, and MQ=10.5. 17. Express each ratio in simplest form. 3p
3(x + 4)
12
52
3a
6a + 12
b.
e.
a.
c.
d.
f.
5p a(x + 4) 20 100 4ab 6 Find x and the measures of the indicated parts. 18. DE, if DE = x+2 19.BD and DC, if ΔBAD∼ΔACD 20. CD, if ΔBAD∼ΔACD and CD = (x-­‐4) 21. AC and CE, if AC=x+4, CE=2x, BD=9, and DF=12 22. BD and DF, if BF=24, BD=x, AC=8, and CE=12