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Geometry/Trig VIDEO LESSON Name: ______________________________ Date: _______________________________ Midterm Review 5 - Parallel Line Theorems (Unit 5) The Learning goals we achieved in these units were… 1. How do we determine if two lines are parallel? 2. What kind of special angles are formed given two parallel lines and a transversal? 3. How can I the relationship between special angles given two lines are parallel? 4. How can I determine if two lines are parallel given two lines and a transversal, and justify my answer? Special Angle Types Vertical angles Supplementary angles Alternate Interior Angles Alternate Exterior Angles Example Description Across from each other over a vertex Relationships Always _______________ Adjacent angles that form a line two angles that add up to ________ degrees Opposite sides of the transversal and inside the lines Opposite sides of the transversal and outside the lines Corresponding angles In the “same position” or “same corner” of the transversal & lines Same-side interior Same side of the transversal and inside the lines Same side exterior angles Justifying that Lines are Parallel Same side of the transversal and outside the lines ________________________ when lines are∥ ________________________ when lines are∥ ________________________ when lines are∥ ________________________ when lines are∥ ________________________ when lines are∥ When justifying parallel lines you need to include 1. Type of angle pair 2. Relationship 3. State if the relationship is true (from diagram) 4. Conclusion 1. In the diagram below, m∠AEC = 3x + 30 and m∠CED = 2x - 5. Find the m∠AEC. Geometry/Trig 2. Using the picture at the right, state the type and relationship for each pair of angles given. Solve if asked. (a) ∠1 𝑎𝑛𝑑 ∠5 Type: __________________________________________________ Relationship if lines ||: ________________________________________ (b) ∠4 𝑎𝑛𝑑 ∠5 Type: __________________________________________________ Relationship if lines ||: ________________________________________ (c) What type of special angle pair are ∠4 and ∠6? __________________________________________________ You are given that m∠4 = 81o. What is the m∠6? (d) You are given that ∠1 = 7x+20 and ∠8 = 9x – 2. What is the m∠8? 3. Investigate the diagram below. Is AB is parallel to CD in the following diagram? EXPLAIN YOUR REASONING Geometry/Trig « « « 4. In the accompanying diagram, AB , CD and EF intersect at G. If ∠𝐷𝐺𝐵 = 20 𝑑𝑒𝑔𝑟𝑒𝑒𝑠 and∠𝐹𝐺𝐶 = 72 𝑑𝑒𝑔𝑟𝑒𝑒𝑠, find the measurement of ∠1, ∠2. ∠3, 𝑎𝑛𝑑 ∠4 ∠1 = ______________ ∠2 = ______________ ∠3 = ______________ ∠4 = ______________ 5. In the accompanying diagram, ⃡𝐴𝐵 ∥ ⃡𝐶𝐷, and transversal ⃡𝐸𝐹 intersects ⃡𝐴𝐶 and ⃡𝐸𝐺 at G and H, respectively. If 𝑚∠𝐵𝐺𝐻: 𝑚∠𝐷𝐻𝐺 𝑎𝑟𝑒 𝑖𝑛 𝑎 𝑟𝑎𝑡𝑖𝑜 𝑜𝑓 3: 6, find 𝑚∠𝐵𝐺𝐻. 6. Solve for angles 1, 2, and 3 in the diagram below. Show your work clearly! m∠1 = ______________________ m∠2 = ______________________ m∠3 = ______________________