Transversal Lines Intersecting Parallel Lines The Angle Measures

Transversal Lines Intersecting Parallel Lines: The Angle Measures of the Angle Pair Relationships Section 3. 2 Big Ideas Geometry

Unit 1 Review � Congruent Angles: two angles that have the same exact measure ◦ If m∠ 1 = m∠ 2, then ∠ 1 ≅ ∠ 2 ◦ If ∠ 1 ≅ ∠ 2, then m∠ 1 = m∠ 2

Unit 1 Review � Vertical Angles: two angles whose sides form two pairs of opposite rays ◦ Remember, vertical means “directly across/opposite” in this case ◦ Vertical angle pairs are congruent to each other, so they have the same measure 4 1 3 2 ∠ 1 ≅ ∠ 3 ∠ 2 ≅ ∠ 4

Unit 1 Review � Angles on a line: all angles on the same side of a line sum to 180° ◦ Addendum - Linear Pairs: Two angles on the same side of the line that sum to 180° � Angles around a point: all angles around a common endpoint sum to 360°

4 Angle Pair Relations � 1. Corresponding Angles: two angles that have corresponding positions � 2. Alternate Interior Angles: two angles that lie in between the two lines and on opposite sides of the transversal t � 3. Alternate Exterior Angles: two angles that lie outside the two lines and on opposite sides of the transversal t � 4. Consecutive Interior Angles: two angles that lie between the two lines and on the same side of the transversal t

The following 4 Theorems will use the diagram below t 1 3 5 7 2 n 4 6 8 m

Corresponding Angles (CA) Theorem � If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent ◦ ∠ 1 ≅ ∠ 5, ∠ 2 ≅ ∠ 6, ∠ 3 ≅ ∠ 7, ∠ 4 ≅ ∠ 8

Alternate Interior Angles (AIA) Theorem � If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent ◦ ∠ 4 ≅ ∠ 5, ∠ 3 ≅ ∠ 6

Alternate Exterior Angles (AEA) Theorem � If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent ◦ ∠ 1 ≅ ∠ 8, ∠ 2 ≅ ∠ 7

Consecutive Interior Angles (CIA) Theorem � If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary ◦ Supplementary: two positive angles whose measures have a sum of 180° ◦ ∠ 3 and ∠ 5 are supplementary, ∠ 4 and ∠ 6 are supplementary

Example #1: Find the remaining 7 angle measurements. Make sure to note how you know the answer is correct t 100° 2 3 5 6 7 8 4 m n

Solution #1: Find the remaining 7 angle measurements. Make sure to note how you know the answer is correct t 100° 80° 100° m 100° 80° 100° n

Example #2: Find the following values: x, y and m∠ 5. What is the reason you got those answers? t n 120° (30 x)° 5 (10 y – 20)° m

Solution #2: Find the following values: x, y and m∠ 5. What is the reason you got those answers? t n 120° (30 x)° m 5 (10 y – 20)° m∠ 5 = 120° x=4 y=8

Challenge: Find the values of x, y, z and complete the diagram. t 1 83° n (7 x-8)° 4 5 (6 y+11)° 6 (4 z+1)° m

Challenge: Find the values of x, y, z and complete the diagram. t 97° 83° n 83° 97° m 97° 83° 97° x = 13 y = 12 z = 24

Bibliography � Big Ideas Geometry