3-3: Proving Lines Parallel Do NOW 2/18/2019 11:31 PM 3-3: Proving Lines Parallel

Page 158 (Answers may vary) 7) 100° 9) 102° 11) 90° 13) 120°, Correspond. Angle Post. 15) 60°, Same-Side Int. Angle Thrm. 17) 60°, Linear Pair Theorem 19) 120°, Vertical Angle Theorem 21) x = 4, Same Side Int. Angle Thrm. Angle 3: 103°, Angle 4: 77° 23) x = 3, Corr. Angle Post. Angle 1 = Angle 4 = 42° 27) 28) Impossible, Same-Side interior angles are supplementary, not complementary 31) Choice A is incorrect because angles are supplementary and not congruent 37) 75° 2/18/2019 11:31 PM 3-3: Proving Lines Parallel

3-3: Proving Lines Parallel 2/18/2019 11:31 PM 3-3: Proving Lines Parallel

Angles with Parallel Line Systems Section 3-3A Geometry PreAP, Revised ©2013 viet.dang@humble.k12.tx.us 2/18/2019 11:31 PM 3-3: Proving Lines Parallel

3-3: Proving Lines Parallel Example 1 Find the value of x in each question given that lines l and m are parallel. Check your answers by finding the measure of each angle given that 𝒎∠𝑪=𝟑𝒙−𝟏𝟎 and 𝒎∠𝑭=𝒙+𝟕𝟎 2/18/2019 11:31 PM 3-3: Proving Lines Parallel

3-3: Proving Lines Parallel Example 2 Find the value of x in each question given that lines l and m are parallel. Check your answers by finding the measure of each angle given that 𝒎∠𝑩=𝟐 𝒙+𝟒𝟎 and 𝒎∠𝑮=𝟓𝒙+𝟒𝟒 2/18/2019 11:31 PM 3-3: Proving Lines Parallel

3-3: Proving Lines Parallel Your Turn Find the value of x in each question given that lines l and m are parallel. Check your answers by finding the measure of each angle given that 𝒎∠𝑫=𝒙+𝟐𝟕 and 𝒎∠𝑭=𝟐𝒙−𝟑𝟗 2/18/2019 11:31 PM 3-3: Proving Lines Parallel

3-3: Proving Lines Parallel Example 3 Given 𝒍∥𝒎, find the value (s) of x and each angle. Check for extraneous solutions. Given: 𝒎∠𝟑= 𝒙 𝟐 +𝟏𝟏𝟐 and 𝒎∠𝟖=𝟏𝟔𝒙+𝟏𝟑𝟏 2/18/2019 11:31 PM 3-3: Proving Lines Parallel

3-3: Proving Lines Parallel Example 4 Given 𝒍∥𝒎, find the value (s) of x and each angle. Check for extraneous solutions. Given: 𝒎∠𝟑= 𝒙 𝟐 −𝟐𝒙 and 𝒎∠𝟔=𝟑𝒙+𝟏𝟎𝟖 2/18/2019 11:31 PM 3-3: Proving Lines Parallel

3-3: Proving Lines Parallel Your Turn Given 𝒍∥𝒎, find the value (s) of x and each angle. Check for extraneous solutions. Given: 𝒎∠𝟏= 𝒙 𝟐 −𝟕𝒙 and 𝒎∠𝟕=−𝒙+𝟕 2/18/2019 11:31 PM 3-3: Proving Lines Parallel

3-3: Proving Lines Parallel Example 5 Given 𝒑∥𝒕, find the value (s) of x and each angle. Check for extraneous solutions. Given: 𝒎∠𝟏=𝟏𝟐𝒙−𝟒𝒚, 𝒎∠𝟖=𝒙−𝟒𝒚, and 𝒎∠𝟓=𝟏𝟓𝒙+𝟖𝒚 2/18/2019 11:31 PM 3-3: Proving Lines Parallel

3-3: Proving Lines Parallel Example 6 Given 𝒑∥𝒕, find the value (s) of x and each angle. Check for extraneous solutions. Given: 𝒎∠𝟐=𝟖𝒃+𝒂, 𝒎∠𝟓=𝟕𝒂+𝟐𝟓𝒃, and 𝒎∠𝟒=𝟑𝒂+𝟓𝒃 2/18/2019 11:31 PM 3-3: Proving Lines Parallel

3-3: Proving Lines Parallel Your Turn Given 𝒑∥𝒕, find the value (s) of x and each angle. Check for extraneous solutions. Given: 𝒎∠𝟑=𝟏𝟒𝒔−𝟑𝒕, 𝒎∠𝟕=𝟗𝒔+𝟏𝟐𝒕, and 𝒎∠𝟒=𝟓𝒔+𝟔𝒕 2/18/2019 11:31 PM 3-3: Proving Lines Parallel

3-3: Proving Lines Parallel Example 7 Given 𝒍∥𝒎. Prove: ∠𝟏 & ∠𝟐 are supplementary Statement Reason 1) 𝒍∥𝒎 Given 2) ∠𝟏≅∠𝟑 Linear Pair Theorem 3) m∠𝟏=𝑚∠𝟑 Def’n of Congruency 4) ∠𝟑 & ∠𝟐 are supplementary Same Side Interior Angle Theorem 5) m∠𝟑+𝑚∠𝟐=𝟏𝟖𝟎° Def’n of Supplementary 6) m∠𝟏+𝑚∠𝟐=𝟏𝟖𝟎° Substitution 7) ∠𝟏 & ∠𝟐 are supplementary 2/18/2019 11:31 PM 3-3: Proving Lines Parallel