Corresponding and Same-Side Interior Angles

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Presentation transcript:

Corresponding and Same-Side Interior Angles Lesson 6 Lines & Angles Corresponding and Same-Side Interior Angles

Warm-Up Draw a pair of parallel lines that are cut by a transversal. Use your diagram from #1 for 2-4. Do not label any angle with more than one number. 2. Label a pair of alternate interior angles 1 and 2. 3. Label a linear pair of angles 3 and 4. 4. Label a pair of vertical angles 5 and 6.

Corresponding and Same-Side Interior Angles Target: Recognize and apply properties of corresponding and same-side interior angles.

Vocabulary Corresponding Angles: Two non-adjacent angles that are on the same side of a transversal with ne angle is outside the two lines and the other angle is inside. Same-Side Interior Angles: Two angles that are on the inside of two lines and are on the same side of the transversal.

Angles of Two Parallel Lines Intersected by a Transversal Alternate exterior angles are congruent. ∠1 ≅ ∠7 ∠2 ≅ ∠8 Alternate interior angles are congruent. ∠4 ≅ ∠6 ∠3 ≅ ∠5 Corresponding angles are congruent. ∠1 ≅ ∠6 ∠2 ≅ ∠5 ∠3 ≅ ∠8 ∠4 ≅ ∠7 Same-Side interior angles are supplementary. m∠4 + m∠5 = 180° m∠3 + m∠6 = 180° 1 2 4 5 6 8 7 3

Example 1 Name the special angle pair relationship between 1 and 2. corresponding angles same-side interior angles

Example 2 Write an equation and solve for x. Corresponding angles have equal measures. 4x + 9 = 117 Subtract 9 from each side. –9 –9 4x = 108 Divide by 4 on each side. 4 4 x = 27 Check the solution by substituting 27 for x in the equation. 4(27) + 9 = 117 108 + 9 = 117 117 = 117✔

Example 3 Write an equation and solve for x. Then find the measure of each identified angle. The lines are parallel so the same-side interior angles are supplementary. (3x + 1) + (3x + 44) = 180 Combine like terms. 6x + 45 = 180 Subtract 45 from each side. – 45 – 45 6x = 135 Divide by 6 on each side. 6 6 x = 22.5 Find the measure of each angle by substituting 22.5 for x. (3x + 1) = (3(22.5) + 1) = (67.5 + 1) = 68.5° (3x + 44) = (3(22.5) + 44) = (67.5 + 44) = 111.5° 68.5 + 111.5 = 180 ✔

Exit Problems Use the diagram. Find the value of x. List the measurements of angles 1 through 6.

Communication Prompt Name all the special angle pairs from this block that you can remember. Circle the angle pairs that are made up of congruent angles.