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
Name Class Date Reteaching 3-5 Parallel Lines and Triangles Triangle Angle-Sum Theorem: The measures of the angles in a triangle add up to 180. In the diagram at the right, ∆ACD is a right triangle. What are m1 and m2? Step 1 Angle Addition Postulate m1 + mDAB = 90 Substitution Property m1 + 30 = 90 Subtraction Property of Equality m1 = 60 Step 2 Triangle Angle-Sum Theorem m1 + m2 + mABC = 180 Substitution Property 60 + m2 + 60 = 180 Addition Property of Equality m2 + 120 = 180 Subtraction Property of Equality m2 = 60 Exercises Find m1. 1. 2. 3. 4. 5. 6. Algebra Find the value of each variable. 7. 8. 9. Prentice Hall Geometry • Teaching Resources Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved. 49 Name Class Date Reteaching (continued) 3-5 Parallel Lines and Triangles In the diagram at the right, 1 is an exterior angle of the triangle. An exterior angle is an angle formed by one side of a polygon and an extension of an adjacent side. For each exterior angle of a triangle, the two interior angles that are not next to it are its remote interior angles. In the diagram, 2 and 3 are remote interior angles to 1. The Exterior Angle Theorem states that the measure of an exterior angle is equal to the sum of its remote interior angles. So, m1 = m2 + m3. What are the measures of the unknown angles? Triangle Angle-Sum Theorem mABD + mBDA + mBAD = 180 Substitution Property 45 + m1 + 31 = 180 Subtraction Property of Equality m1 = 104 Exterior Angle Theorem mABD + mBAD = m2 Substitution Property 45 + 31 = m2 Subtraction Property of Equality 76 = m2 Exercises What are the exterior angle and the remote interior angles for each triangle? 10. 11. 12. exterior: exterior: exterior: interior: interior: interior: Find the measure of the exterior angle. 13. 14. 15. Prentice Hall Geometry • Teaching Resources Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved. 50