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Angles and Parallel Lines When parallel lines get crossed by another line a line called a transversal, several special angles are formed. These angles can be made into pairs of angles which have special names. When lines are parallel alternate interior and corresponding angles are CONGRUENT. Below, lines l and m are parallel and cut by the transversal t. Two Special Angle Pairs Two Special Angle Pairs Name Congruent Angles Description Alternate Interior Angles 4 5 and 3 6 On the opposite sides of the transversal and on the inside of the given lines. Two Special Angle Pairs Name Congruent Angles Description Alternate Interior Angles 4 5 and 3 6 On the opposite sides of the transversal and on the inside of the given lines. Corresponding Angles 1 5 and 2 6 4 8 and 3 7 On the same side of the transversal and on the same side of the given lines Example Proof: If two parallel lines are cut by a transversal, the alternate interior angles are congruent. Given m is parallel to l, prove: ∠3 = ∠6 Statement Reason Lines l and m are parallel Given Example Proof: If two parallel lines are cut by a transversal, the corresponding angles are congruent. Given m is parallel to l, prove: ∠3 = ∠6 Statement Reason Lines l and m are parallel Given ∠3= ∠7 Corresponding Angles Theorem Example Proof: If two parallel lines are cut by a transversal, the corresponding angles are congruent. Given m is parallel to l, prove: ∠3 = ∠6 Statement Reason Lines l and m are parallel Given ∠3= ∠7 Corresponding Angles Theorem ∠6= ∠7 Vertical Angles Example Proof: If two parallel lines are cut by a transversal, the corresponding angles are congruent. Given m is parallel to l, prove: ∠3 = ∠6 Statement Reason Lines l and m are parallel Given ∠3= ∠7 Corresponding Angles Theorem ∠6= ∠7 Vertical Angles ∠3= ∠6 Transitive Property Solve for x: Solve for x: -10 + 8x = 7x - 10 = -x 10 = x Check our Answer: -10 + 8(10) = 70 degrees and 7(10) =70 deg The angles are Corresponding so their angle measures should be equal. Solve for x: Solve for x: 12x + 1 = 11x + 9 x+1 =9 x =8 Check our Answer: 12(8) + 1 = 97 degrees and 11(8) + 9 = 97 deg The angles are alternate interior so their angle measures should be equal.