1 / 8

Applications of Similar Triangles

Applications of Similar Triangles. Definition of similarity Solving for unknowns Application problems. Two triangles are considered to be similar if and only if:. they have the same shape. corresponding angles are equal.

uma-marks
Download Presentation

Applications of Similar Triangles

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Applications of Similar Triangles • Definition of similarity • Solving for unknowns • Application problems

  2. Two triangles are considered to be similar if and only if: • they have the same shape • corresponding angles are equal • the ratio of the corresponding side lengths are equal

  3. F C x 1 m A B D E 72 cm 18.5 m Ex #1: To estimate the height of a tree, Margaret held a metre stick perpendicular to the ground and observed the length of its shadow was 72 cm. Then she measured the length of the tree’s shadow as 18.5 m. What was the approximate height of the tree? Step 1: Draw a labeled diagram. Step 2: Identify two similar triangles.  ABC ~  DEF Step 3: Write equivalent ratios

  4. F C x 1 m A B D E 72 cm 18.5 m Step 4: Use the ratios that apply to solve for x. 0.72x = 18.5 x = 25.7 m

  5. Ex #2: Surveyors have laid out triangles to find the length of a lake. Calculate this length, AB. ft Step 1: Draw a labeled diagram. PROVIDED ft Step 2: Identify two similar triangles. ft  ACB ~  ECD Step 3: Write equivalent ratios

  6. Step 4: Use the ratios that apply to solve for x. ft ft ft

  7. D F C Ex #3: On a camping expedition, two campers decide to calculate the length of the small lake just beside their campsite. They mark off a 2 m line parallel to the shore of the lake. Then, they step back from the line until they can site each end of the lake with one end of the line they have marked. From this position, they can measure the distance to one end of the 2 m line [3.1 m]. The distance to the corresponding end of the lake is indicated on a bike trail sign [1200 m]. How long is the lake? Step 1: Draw a labeled diagram. PROVIDED Step 2: Identify two similar triangles.  ABC ~  DFC

  8. D F C Step 3: Write equivalent ratios In  ABC ~  DFC, Step 4: Use the ratios that apply to solve for x. 3.1(AB) = 2400 x = 774.19 m

More Related