Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
UNIT 8 MIXED REVIEW Assessment readiness 1. Determine whether each pair of angles is a pair of vertical angles, a linear pair of angles, or neither. Select the correct answer for each lettered part. C • Online Homework • Hints and Help • Extra Practice D B E F A A. ∠AFC and ∠CFD Vertical Vertical Vertical B. ∠AFB and ∠CFD C. ∠BFD and ∠AFE Linear Pair Linear Pair Linear Pair Neither Neither Neither 2. Does each transformation map a triangle in Quadrant II to Quadrant I? Select Yes or No for A–C. Yes No A. A rotation of 270° B. A translation along the vector (-2, -2) Yes No C. A reflection across the y-axis Yes No © Houghton Mifflin Harcourt Publishing Company 3. Are the triangles necessarily congruent? Select Yes or No for each statement. D 75° 5.7 cm A 42° F 63° 6.2 cm B C 8.1 cm A. AC = 5.7 cm B. m∠BAC = 75°, m∠ABC = 63°, and DE = 6.2 cm C. m∠ACB = 42°, m∠ABC = 63°, and FE = 8.2 cm Unit 8 1181 Yes Yes Yes No No No E 4. Triangle △ABC is in the second quadrant and translated along (-3, 2)and reflected across the y-axis. Determine if the translation will be in the given quadrant. Select Yes or No for each statement. A. In the first quadrant after the first transformation Yes No B. In the second quadrant after the first transformation Yes No C. In the third quadrant after the second transformation Yes No _ _ , 5. Given △ABC where A(2, 3), B(5, 8_ ), C(8, 3_ ), RS is the midsegment parallel to AC _ ST is the midsegment parallel to AB , and RT is the midsegment parallel to _ BC , determine if the statements are true or false. Select True or False for each statement. _ A. ST = 4 True False _ B. RT = 5 True False _ C. RS = 3 True False 6. Find each angle measure. Y X 68° Z 128° ℓ m Statements Unit 8 Reasons 1182 t 1 2 3 4 5 6 7 8 © Houghton Mifflin Harcourt Publishing Company 7. Write a proof in two-column form for the Corresponding Angles Theorem. Given: ℓ∥m Prove: m∠3 = m∠7 Performance Tasks 8. An employee is walking home from work and wants to take the long way to get more exercise. The diagram represents the two different routes, where A is the employee’s work and B is the employee’s home. Which route is longer and by how much? Show your work. 3.8 miles A 2.1 miles B 9. A student was given the following triangle and asked to find the circumcenter. Find the point and explain the steps for finding it. y C (6, 7) 6 4 A (-1, 2) © Houghton Mifflin Harcourt Publishing Company 0 10. While constructing a roof, a construction company built a triangle frame with a base 25 feet long. A cross bar needs to be inserted that connects the midpoints of both sides of the frame. Draw an image to represent the situation and then describe how much wood is needed for the crossbar. Assume the triangle is isosceles. Explain your answer. Unit 8 1183 B (6, 2) 2 4 6 x math in careers Architect An architect is writing the blueprints for a large triangular building to go in the middle of a city. The building needs to be congruent to a building that is already made, but the blueprints for the previous building were lost. What information will need to be known about each triangular face of the building in order to make sure all faces are congruent, knowing the building does not have any right triangles? Explain each possibility using known triangle congruence theorems and postulates. © Houghton Mifflin Harcourt Publishing Company Unit 8 1184