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

2. Warm-Up Draw a pair of parallel lines that are cut by a transversal.
Use your diagram from #1 for 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.

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

4. 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.

6. 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

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

8. 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✔

9. 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) = ( ) = 68.5° (3x + 44) = (3(22.5) + 44) = ( ) = 111.5°
= 180 ✔

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

11. 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.