5.2 Proving That Lines Are Parallel Advanced Geometry 5.2 Proving That Lines Are Parallel Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by a transversal to prove that lines are parallel. Learner Objective: Students will be able to use angles formed by a transversal to prove that two lines are parallel. MA-HS-3.1.3 Students will analyze and apply angle relationships (e.g., linear pairs, vertical, complementary, supplementary, corresponding and alternate interior angles) in real-world and mathematical situations.
Given: M is the midpoint of Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by a transversal to prove that lines are parallel. Warm-Up Given: M is the midpoint of Prove: K N W L M
Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by a transversal to prove that lines are parallel. Given lines m and n cut by transversal t: Name the pairs of alternate interior angles. Name the pairs of corresponding angles. Name the pairs of alternate exterior angles. Name pairs of angles that are interior angles on the same side of the transversal. Name pairs of angles that are exterior angles on the same side of the transversal. 2 1 3 4 5 6 7 8 m n t
Exterior Angle of a triangle Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by a transversal to prove that lines are parallel. Exterior Angle of a triangle An Exterior Angle of a triangle is formed whenever a sided of the triangle is extended to form an angle supplementary to the adjacent interior angle. A B C D Remote Interior Angles Exterior Angle The other two interior angles are referred to as Remote Interior Angles. Adjacent Interior Angle
Exterior Angle Inequality Theorem Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by a transversal to prove that lines are parallel. Exterior Angle Inequality Theorem The measure of an exterior angle of a triangle is greater than the measure of either remote interior angle. A B C D
Learner Objective: Students will be able to use angles formed by a transversal to prove that two lines are parallel. Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by a transversal to prove that lines are parallel.
Learner Objective: Students will be able to use angles formed by a transversal to prove that two lines are parallel. Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by a transversal to prove that lines are parallel.
Learner Objective: Students will be able to use angles formed by a transversal to prove that two lines are parallel. Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by a transversal to prove that lines are parallel.
Learner Objective: Students will be able to use angles formed by a transversal to prove that two lines are parallel. Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by a transversal to prove that lines are parallel.
Learner Objective: Students will be able to use angles formed by a transversal to prove that two lines are parallel. Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by a transversal to prove that lines are parallel.
Learner Objective: Students will be able to use angles formed by a transversal to prove that two lines are parallel. Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by a transversal to prove that lines are parallel.
Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by a transversal to prove that lines are parallel.
Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by a transversal to prove that lines are parallel.
Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by a transversal to prove that lines are parallel.
Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by a transversal to prove that lines are parallel.
Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by a transversal to prove that lines are parallel.
Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by a transversal to prove that lines are parallel.
Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by a transversal to prove that lines are parallel.
Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by a transversal to prove that lines are parallel.
Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by a transversal to prove that lines are parallel.
Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by a transversal to prove that lines are parallel.
Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by a transversal to prove that lines are parallel.
Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by a transversal to prove that lines are parallel.
Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by a transversal to prove that lines are parallel.
Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by a transversal to prove that lines are parallel.
Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by a transversal to prove that lines are parallel.
Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by a transversal to prove that lines are parallel.
Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by a transversal to prove that lines are parallel.
Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by a transversal to prove that lines are parallel.
Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by a transversal to prove that lines are parallel.
Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by a transversal to prove that lines are parallel.
Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by a transversal to prove that lines are parallel.
Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by a transversal to prove that lines are parallel.
Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by a transversal to prove that lines are parallel.
Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by a transversal to prove that lines are parallel.
Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by a transversal to prove that lines are parallel.
Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by a transversal to prove that lines are parallel.
Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by a transversal to prove that lines are parallel.
Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by a transversal to prove that lines are parallel.
Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by a transversal to prove that lines are parallel.
Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by a transversal to prove that lines are parallel.
Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by a transversal to prove that lines are parallel.
Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by a transversal to prove that lines are parallel.
Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by a transversal to prove that lines are parallel.
Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by a transversal to prove that lines are parallel.
Learner Objective: Students will apply the Exterior Angle theorem and will use angles formed by a transversal to prove that lines are parallel.
Learner Objective: Students will be able to use angles formed by a transversal to prove that two lines are parallel.
Learner Objective: Students will be able to use angles formed by a transversal to prove that two lines are parallel.
Learner Objective: Students will be able to use angles formed by a transversal to prove that two lines are parallel.
Learner Objective: Students will be able to use angles formed by a transversal to prove that two lines are parallel.
Learner Objective: Students will be able to use angles formed by a transversal to prove that two lines are parallel.
Learner Objective: Students will be able to use angles formed by a transversal to prove that two lines are parallel.
Learner Objective: Students will be able to use angles formed by a transversal to prove that two lines are parallel.
Learner Objective: Students will be able to use angles formed by a transversal to prove that two lines are parallel.
Learner Objective: Students will be able to use angles formed by a transversal to prove that two lines are parallel.
Learner Objective: Students will be able to use angles formed by a transversal to prove that two lines are parallel.
Learner Objective: Students will be able to use angles formed by a transversal to prove that two lines are parallel.
Learner Objective: Students will be able to use angles formed by a transversal to prove that two lines are parallel.
Learner Objective: Students will be able to use angles formed by a transversal to prove that two lines are parallel.
Learner Objective: Students will be able to use angles formed by a transversal to prove that two lines are parallel.
Learner Objective: Students will be able to use angles formed by a transversal to prove that two lines are parallel.
Learner Objective: Students will be able to use angles formed by a transversal to prove that two lines are parallel.
Name: _______________________ State the theorem that proves lines a and b or lines c and d parallel. 1. __________________________ __________________________ 2. __________________________ __________________________ 3. __________________________ __________________________ 4. __________________________ __________________________ 5. __________________________ __________________________