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Name: __________________________________________ Unit 1: Transformations and Angles Date: ___________________________ Lesson #1: Identify Angle Relationships in Parallel Lines Cut By A Transversal When two _____________________________________ lines are cut by a third line, called the ______________________________________, some special angle relationships are formed. From our exploration we know that… 1 _____________ 2 _____________ 5 _____________ 6 _____________ 1 + 2 = _____________ 1 + 3 = _____________ How many other angles are supplementary to 1? _______________________________ How many other angles are congruent to 1?_______________________________ CORRESPONDING ANGLES (WHEN YOU SLIDE ‘EM, THEY TAKE THE SAME SPOT!) Since corresponding angles are the same shape and 1 3 5 7 2 4 6 8 same size, we know they are ___________________________________________. That means their angle measures are ___________________________________________. 1 corresponds to _______________ 5 corresponds to _______________ 2 corresponds to _______________ 6 corresponds to _______________ 3 corresponds to _______________ 7 corresponds to _______________ 4 corresponds to _______________ 8 corresponds to _______________ 1 Name: __________________________________________ Unit 1: Transformations and Angles Date: ___________________________ Lesson #1: Identify Angle Relationships in Parallel Lines Cut By A Transversal ALTERNATE INTERIOR ANGLES (A.I.A.) Alternate Interior Angles are ______________________________. “Alternate” refers to the angles being on ______________________________ sides of the transversal. “Interior” refers to the angles being on the ______________________________ of the parallel lines. Statement Reason A = 35 Given Information D A H E A C B G F ≅ G So, we can conclude that if two angles are alternate interior angles, their measures are the ____________. ALTERNATE EXTERIOR ANGLES (A.E.A.) Alternate Exterior Angles are ______________________________. “Alternate” refers to the angles being on ______________________________ sides of the transversal. “Exterior” refers to the angles being on the _______________________________ of the parallel lines. 2 Name: __________________________________________ Unit 1: Transformations and Angles Date: ___________________________ Lesson #1: Identify Angle Relationships in Parallel Lines Cut By A Transversal Statement Reason C = 40 Given Information D A H E C C B G F ≅ E So, we can conclude that if two angles are alternate exterior angles, their measures are the ____________. Example 1: Find Angle Measures of Parallel Lines Cut by Transversals In the figure, line a line b. Find the measure of each angle. What is the measure of 4? What is the measure of 3? What is the measure of 5? 3 Name: __________________________________________ Unit 1: Transformations and Angles Date: ___________________________ Lesson #1: Identify Angle Relationships in Parallel Lines Cut By A Transversal You Try 1! In the figure, line m line l. Find the measure of each angle. What is the measure of 4? What is the measure of 2? What is the measure of 6? How many different angles would be formed by a transversal intersecting three parallel lines? How many different angle measures would there be? _______________________________________________________________________________________ _______________________________________________________________________________________ _______________________________________________________________________________________ Explain how a transversal could intersect two other lines so that corresponding angles are not congruent. _______________________________________________________________________________________ _______________________________________________________________________________________ _______________________________________________________________________________________ Can you think of two real-world examples of parallel lines? How are these examples different from the mathematical concept of parallel lines? _______________________________________________________________________________________ _______________________________________________________________________________________ _______________________________________________________________________________________ _______________________________________________________________________________________ _______________________________________________________________________________________ 4 Name: __________________________________________ Unit 1: Transformations and Angles Date: ___________________________ Lesson #1: Identify Angle Relationships in Parallel Lines Cut By A Transversal Exit Ticket: 1. Name all angles congruent to 3. 2. Name all the angles supplementary to 6. 3. If m 1 = 105, what is the m 3? 4. If m 5 = 120, what is the m 2? 5