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Name: ________________________ Geometry – Mr. Lewis Date: __________________________ What can parallel lines and linear pairs tell us? Directions: Copy the diagram above into your notebook or graph paper. Use up as much space as possible, Label the points EXACTLY AS SHOWN! Use the lines on your paper to make sure that AB is parallel to CD. Given: ⃡𝐴𝐵 ∥ ⃡CD (This statement says Line AB is parallel to Line CD) 1. Use your protractor to measure ∠ GEB and ∠ EFD a. m∠ GEB = ______° b. m ∠ EFI = ______° 2. Is this the result that was expected? 3. What is this type of angle pair called? 4. Use linear pairs to find the remaining angles without your protractor! a. m∠ FEA = ______° c. m∠ HFI = ______° b. m∠ HFC = ______° d. m∠ EFC = ______° 5. All the acute angles in this diagram are congruent. True False 6. All the obtuse angles in this diagram are congruent. True False Name: ________________________ Geometry – Mr. Lewis Date: __________________________ Proof of the Triangle Sum Theorem Using the same diagram from page 1, Use a ruler to connect points E and I. Extend this line as far as possible. 7. Use a protractor to find the measure of ∠ BEI. __________ 8. Angles ∠ FEA, ∠ FEI, and ∠ BEI are (choose one) a) Complementary b) Vertical c) Supplementary d) Alternate exterior 9. m ∠ EIF = m ∠ BEI (Explain your choice) True False 10. Determine, without a protractor, the measure of ∠ FEI. _________ Explain your reasoning. 11. Fill in the blanks. m∠ EFI = _____° m∠ FEI = ____° m∠ EIF = ______° 12. Does triangle EFI follow the “Triangle Sum Theorem”? Explain. Statement – Reason Practice 13. Write a statement – reason proof that shows the value of all angles 1-12. Be sure to use proper vocabulary. Ex: Statement Reason ∠ 1 = 120° Vertical Angles are congruent. ∠ 2 = 60° Supplementary Angles add up to 180° Continue…. Name: ________________________ Geometry – Mr. Lewis Date: __________________________ Midpoint, Mid-segment and Side-splitter Theorem Directions: Copy the diagram above into your notebooks. Answer the questions below. If you choose TRUE as an answer, name the theorem that makes your answer true. Given: Segment FE is the mid-segment of triangle ABC. Point D is the midpoint of BC 14. Point F is the midpoint of AB. True False 15. FE = BD True False 16. AE = FB True False 17. FE ∥BC (Parallel) True False 18. Name two pairs of congruent angles in the image above. Given: m∠ FAE = 75° and m∠ FEC = 120° 19. Use the “Exterior Angle Theorem” and the given information to determine m∠ AFE. 20. Find the measure of the remaining angles, justify each answer. m∠AEF = _____° m∠BFE = _____° m∠ECB = _____° m∠FBD = _____° Given: AF = 5.6 ft., EC = 4.5 ft., and BC = 12.5 ft. Label all missing measurements. 21. Find the perimeter of Triangle AFE (SHOW ALL STEPS) 22. Find the perimeter of Quadrilateral BFEC. (SHOW ALL STEPS)