3.5.4 Test (TS): Right Triangles Test Geometry Sem 1 (S3537251) Points possible: 50 Julio Duenas Date: ____________ Answer the following questions using what you've learned from this unit. Write your answers in the space provided. Be sure to show all work. 1. Find the area of a triangle with the given vertices. Part I: Graph the following points on the coordinate grid below. (3 points) (1, -3), (3, -1), (5, -3) Part II: Find the area of the triangle. Show your work. (4 points) 2. The South Memorial School is designing a new playground. There will be a walkway that diagonally crosses the square playground. The walkway is 55 meters long. Part I: Include a sketch of the playground and find the length of one side. Round your answer to the nearest 10th. Show your work. (3 points) 38.9 Part II: Use your answer from Part I to find the perimeter of the playground. Round your answer to the nearest 10th. Show your work. (3 points) 38.9 x 4=155.6 3. Ken leans a 12-foot ladder against his house. He places the ladder so that the base is 5 feet from the house. How far up the house does the ladder reach? Part I: Sketch and label a figure that illustrates the scenario above. (3 points) Part II: Set up an equation to find how far up the house the ladder reaches, and solve the equation. Round your answer to the nearest 10th. Show your work. (3 points) 4. An equilateral triangle has sides that are 8 inches long. Part I: Draw an equilateral triangle with side lengths of 8 inches. (2 points) Part II: Find the area of the triangle that you drew in Part I. Leave your answer in simplest radical form. Show your work. (5 points) 5. On the square baseball diamond shown below, the distance from first base to second base is 90 feet. How far does the catcher have to throw the ball from home plate to reach second base? Round your answer to the nearest 10th. Show your work. (5 points) 6. Mia is warming up before dance class. She sometimes places an elastic band around her calves to add resistance to her warm-up. Part 1: Label points A, B, and C on the triangle. (3 points) Given: In to AC. , DE is parallel Part 2: Use the spaces provided below to complete a formal proof. (5 points) Given: In , DE is parallel to AC Prove: Statements 1. DE is parallel to AC Reasons 1. Given 2. Conclusion from Statement 1 3. A transversal line creates corresponding congruent angles 4. An angle is congruent to itself 5. ABC ~ DBE 6. SSS similarity theorem 7. Rex, Paulo, and Ben are standing on the shore watching for dolphins. Paulo sees one surface directly in front of him about a hundred feet away. Use the spaces provided below to prove that the square of the distance between Rex and Ben is the same as the sum of the squares of the distances between Rex and the dolphin, and Ben and the dolphin. (11 points, 1 per blank) Statements Reasons 1. ADC ~ ACB 2. The ratio of corresponding sides of similar triangles is a constant. 3. Rewrite statement 2 using given side labels. 4. b2 = ce 5. BDC ~ BCA 6. 7. Given 8. Cross multiply statement 7. 9. Add statements 4 and 8. 10. c is a common factor. 11. a2 + b2 = c2