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?