Download Chapter 6: Similar Triangles Topic 4: Ratios of Similarity Part II

Name:___________________________________________
Date:________ Period:_______
Chapter 6: Similar Triangles
Topic 4: Ratios of Similarity Part II
Sometimes, instead of being asked to find the ratio of the perimeters, areas, or volumes, we are asked to find
the perimeter/area/volume for a specific shape. To do this, we must find the given similarity ratio and then set
up a __________________________.
Examples:
1. The ratio of the surface areas of two similar prisms is 25:36. What is the perimeter of the smaller
prism if the perimeter of the larger prism is 56 cm. Round to the nearest tenth, if necessary.
2. The ratio of the volumes of two similar spheres is 125:512. Find the surface area of the larger
sphere if the surface area of the smaller sphere is 3200 m2. Round to the nearest tenth, if necessary.
3. The length of the sides of two triangles are in the ratio of 6:7. If the area of the larger triangle is 45
cm2, find the area of the smallest triangle to the nearest hundredth.
4. The ratio of the areas of two rectangles is 4:121. Find the perimeter of the larger rectangle is the
perimeter of the smaller rectangle is 62 inches. Round to the nearest hundredth.
5. The ratio of the sides of two similar triangles is 5:6. If the area of the smaller triangle is 50 km2,
what is the area of the larger triangle?
6. The ratio of the surface areas of two similar cylinders is 144:100. Find the volume of the larger
cylinder to the nearest tenth if the volume of the smaller cylinder is 75 m 3.
Name:___________________________________________
Date:________ Period:_______
Similarity Ratios Day 2: HW
Homework Examples:
1.) If the ratio of the perimeters of two cubes is 5:7, find the volume of the larger cube if the volume of the
smaller cube is 486 m3. Round to the nearest tenth.
2.) If the ratio of the volumes of two spheres is 343:729, find the area of the smaller sphere if the surface area
of the larger sphere is 198 cm2. Round to the nearest tenth.
3.) Triangle RST is similar to triangle XYZ with RS = 3 inches and XY = 2 inches. If the area of triangle RST is 27
square inches, determine and state the area of triangle XYZ, in square inches.
4.) The sides of a triangle are 8, 12, and 15. The longest side of a similar triangle is 18. What is the
ratio of the perimeter of the smaller triangle to the perimeter of the larger triangle?
(1) 2:3
(2) 4:9
(3) 5:6
(4) 25:36
Review Questions:
5.) In the diagram below of quadrilateral ABCD, E and F are points on ̅̅̅̅
𝐴𝐵 and ̅̅̅̅
𝐶𝐷 , respectively, ̅̅̅̅
𝐵𝐸 ≅
̅̅̅̅
̅̅̅̅
̅̅̅̅
𝐷𝐹 , and 𝐴𝐸 ≅ 𝐶𝐹 . Which conclusion can be proven?
(1) ̅̅̅̅
𝐸𝐷 ≅ ̅̅̅̅
𝐹𝐵
̅̅̅̅ ≅ 𝐶𝐷
̅̅̅̅
(2) 𝐴𝐵
(3) ∠𝐴 ≅ ∠𝐶
(4) ∠𝐴𝐸𝐷 ≅ ∠𝐶𝐹𝐵
⃡
6.) In the diagram below 𝑅𝐶𝐵𝑇
and ∆𝐴𝐵𝐶 are shown with 𝑚∠𝐴 = 60 and 𝑚∠𝐴𝐵𝑇 = 125. What is 𝑚∠𝐴𝐶𝑅?
(1) 125
(2) 115
(3) 65
(4) 55
7.) A transversal intersects two lines. Which condition would always make the two lines parallel?
(1) Vertical angles are congruent.
(2) Alternate interior angles are supplementary.
(3) Corresponding angles are congruent.
(4) Same-side interior angles are complementary.
8.) In right triangle DEF, 𝑚∠𝐷 = 90 and 𝑚∠𝐹 is 12 degrees less than twice 𝑚∠𝐸. Find 𝑚∠𝐹.