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
Riemannian connection on a surface wikipedia , lookup
Geometrization conjecture wikipedia , lookup
Trigonometric functions wikipedia , lookup
Perspective (graphical) wikipedia , lookup
Rational trigonometry wikipedia , lookup
Multilateration wikipedia , lookup
History of geometry wikipedia , lookup
Line (geometry) wikipedia , lookup
Geometry/Trig +Name: ______________________________ Date: _______________________________ Lesson 5-6: Proving Lines Parallel Day 2 Learning Goal: #3: How can we justify whether or not lines are parallel using angles? Warm up 1. Let’s look at the following student work and answer the questions below: The m∠1 = 59 degrees and m∠8 = 59 degrees. Justify whether or not x and y are parallel. What did Meredith do well in this problem Wha What suggestions could we give to and in her explanation? Meredith to improve her explanation? Let’s try one: 2. Is line A parallel to line B? Justify your answer! The labeled angles are __________________________ (type), therefore, they must be ________________________ (relationship) when the lines are parallel. The angles are _________________________, so the lines ___________________ parallel. Geometry/Trig ̅̅̅̅ is parallel to 𝐶𝐷 ̅̅̅̅ . 1. Use the information provided in the picture below to prove that 𝐴𝐵 HINT: Use the triangles to help you fill in some missing angles! Can you identify/use any angle relationships? Practice 2. Is AB parallel to CD? Justify your answer! Remember to write a clear and thorough explanation! Use the model in our notes to help us!! 3. Find the value of x that would make a parallel to b. Explain how you arrived at your answer. Geometry/Trig 4. Determine whether each pair of lines is parallel. Be sure to justify your answer! (a) 5. Find the measure of angles 1, 2, and 3. 𝑚∠1 = 𝑚∠2 = 𝑚∠3 = 6. Solve for x: (b) Geometry/Trig 7. Using the information provided in the diagram and your knowledge of angles, find the measure of ALL missing angles. 𝑚∠1 = 𝑚∠7 = 𝑚∠2 = 𝑚∠8 = 𝑚∠3 = 𝑚∠9 = 𝑚∠4 = 𝑚∠10 = 𝑚∠5 = 𝑚∠11 = 𝑚∠6 = 𝑚∠12 = 8. Two vertical angles measure x and 45°. How many degrees are there in x? 9. Two complementary angles measure x and 65°. How many degrees are there in x? 10. Using the diagram below…Don’t forget to use three letters!! (a) Name a pair of supplementary angles. (b) Name a pair of vertical angles. Geometry/Trig 11. Solve for angles a, b, c in the diagram below. Show your work clearly! 12. Solve for the missing angle. Show your work clearly!