geometry honors name: unit 7 day 1 hw...
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Geometry Honors Name:_____________________ Unit 7 Day 1 HW Date:______________________ 460-463; 13, 15, 18, 26, 27, 29 1. The ratio of the measures of the three sides of a triangle is 9: 7: 5. Its perimeter is 191.1 inches. Find the measure of each side. 2. The ratio of the measures of the three sides of a triangle is !
!: !!: !!. Its
perimeter is 4.75 feet. Find the measure of each side. 3. Find the measures of the angles of a triangle if the ratio of the measurements of the three angles is 7: 5: 8. 4. Solve the proportions:
a. !!!!!!
= !!
b. !!!!!
= !!!!!
5. According to a study done by Lizzy, 7 out of every 500 Americans aged 13 to 17 years are a vegetarian. In a group of 350 13- to 17-year-olds, about how many would you expect to be vegetarian?
32, 36, 49; 469-473; 10, 12, 13 6. Solve the proportion. Round to the nearest tenth.
𝑥! + 4𝑥 + 440 =
𝑥 + 210
7. The ratio of the measures of the sides of the lengths of a quadrilateral is 2: 3: 5: 4. Its perimeter is 154 feet. Find the length of the shortest side. 8. Compare and contrast ratios and proportions. Explain how you use both to solve a problem. 9. List all pairs of congruent angles and write a proportion that relates the corresponding sides for the given shape.
𝐴𝐵𝐷𝐹 ~ 𝑉𝑋𝑍𝑇 10. Determine whether each pair of figures is similar. If so, write the similarity statement.
a.
b.
21, 22, 24, 26, 27, 35 11. The two polygons are similar. Find the value of 𝑥. 12. Rectangle 𝐴𝐵𝐶𝐷 has a width of 8 yards and a length of 20 yards. Rectangle 𝑄𝑅𝑆𝑇, which is similar to 𝐴𝐵𝐶𝐷, has a length of 40 yards. Find the scale factor of rectangle 𝐴𝐵𝐶𝐷 to 𝑄𝑅𝑆𝑇 and the perimeter of each rectangle. 13. Find the perimeter of △𝑊𝑍𝑋, if △𝑊𝑍𝑋~ △ 𝑆𝑅𝑇, 𝑆𝑇 = 6, 𝑊𝑋 = 5, and the perimeter of △ 𝑆𝑅𝑇 = 15.
14. Find the perimeter of △ 𝐷𝐸𝐹, if △ 𝐷𝐸𝐹~ △ 𝐶𝐵𝐹, perimeter of △ 𝐶𝐵𝐹 = 27, 𝐷𝐹 = 6, 𝐹𝐶 = 8. 15. Two similar rectangles have a scale factor of 2: 4. The perimeter of the large rectangle is 80 meters. Find the perimeter of the small rectangle. 16. Find the value of each variable.
38, 40-45, 48, 51 17. For the given vertices, determine whether rectangle 𝐴𝐵𝐶𝐷 is similar to rectangle 𝑊𝑋𝑌𝑍. Justify your answer.
𝐴 −5,1 ,𝐵 7,5 ,𝐶 7,−1 ,𝐷(−1,−1) 𝑊 −2,10 ,𝑋 14,10 ,𝑌 14,−2 ,𝑍(−2,−2)
18. Determine whether the polygons are always, sometimes, or never similar. Explain your reasoning. a. two obtuse triangles b. a trapezoid and a parallelogram c. two right triangles d. a scalene triangle and an isosceles triangle e. two isosceles triangles f. two equilateral triangles 19. For what value(s) of 𝑥 is 𝐵𝐸𝐹𝐴~ 𝐸𝐷𝐶𝐵?
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