3.1 – Identify pairs of lines and Angles Geometry Chapter 3 3.1 – Identify pairs of lines and Angles

Warm-Up 1.) Parallel Lines 2.) Skew Lines 3.) Parallel Planes Using your own knowledge, or by using your Chromebooks, find the definitions of these terms. 1.) Parallel Lines 2.) Skew Lines 3.) Parallel Planes

Identify Pairs of Lines and Angles Objective: Students will be able to identify angle pairs formed by intersecting lines. Agenda Parallel/Perpendicular Lines Transversals (w/Angles) Examples

Vocabulary – Parallel Lines Definition: Lines that are coplanar and do not intersect. Picture: 𝒎 𝒏 Notation: 𝒎∥ 𝒏 Knowledge Connection: What examples of parallel lines are there in the real world?

Vocabulary – Skew Lines Definition: Lines that are not coplanar and do not intersect. Picture: 𝒎 𝒌 Knowledge Connection: What examples of skew lines are there in the real world.

Vocabulary – Parallel Planes Definition: Planes that do not intersect. Picture: Notation: 𝑷𝒍𝒂𝒏𝒆 𝑨∥ 𝑷𝒍𝒂𝒏𝒆 𝑩 𝑨 𝑩 Knowledge Connection: What examples of parallel lines are there in the real world.

For the Postulates List Postulate 13: The Parallel Postulate If there is a line and a point not on the line, then there is exactly one line through the point that is parallel to the given line. Picture 𝑷 𝒔 𝒓

For the Postulates List Postulate 14: The Perpendicular Postulate If there is a line and a point not on the line, then there is exactly one line through the point that is perpendicular to the given line. Picture 𝒓 𝑷 𝒔

Vocabulary - Transversal Definition: A transversal is a line that intersects two or more coplanar lines at different points. Picture: Line 𝒕 is the transversal of lines 𝒎 and 𝒏 𝒕 𝒎 𝒏 Knowledge Connection: What examples of transversals are there in the real world?

Vocabulary – corresponding angles Definition: Angles that have corresponding positions. Picture: Knowledge Connection: What does it mean to have corresponding positions? 1 2 <1 and <2 are corresponding angles

Vocabulary – alternate interior angles Definition: Angles that lie between the two lines, and are on opposite sides of the transversal. Picture: Knowledge Connection: What does it mean to alternate? To be in the interior? 3 4 <3 and <4 are alternate interior angles

Vocabulary – alternate exterior angles Definition: Angles that lie outside the two lines, and are on opposite sides of the transversal. Picture: Knowledge Connection: What does it mean to alternate? To be in the exterior? 5 6 <5 and <6 are alternate exterior angles

Vocabulary – consecutive interior angles Definition: Angles that lie between the two lines, but are on the same side of the transversal. Picture: Knowledge Connection: What does it mean to be consecutive? To be in the interior? 7 8 <7 and <8 are consecutive interior angles

Practice – Identify Angle Relationships Classify the pair of numbered angles 5 1 Corresponding Angles

Practice – Identify Angle Relationships Classify the pair of numbered angles 6 4 Consecutive Interior Angles

Practice – Identify Angle Relationships Classify the pair of numbered angles 8 3 Alternate Interior Angles

Practice – Identify Angle Relationships Classify the pair of numbered angles 7 2 Alternate Exterior Angles

Practice – Identify Angle Relationships Identify the following pairs from the given diagram Corresponding Alternate Interior Alternate Exterior Consecutive Interior 7 8 6 5 4 3 2 1 <𝟏 𝒂𝒏𝒅<𝟓 <𝟐 𝒂𝒏𝒅<𝟕 <𝟏 𝒂𝒏𝒅<𝟖 <𝟐 𝒂𝒏𝒅<𝟓 <𝟑 𝒂𝒏𝒅<𝟔 <𝟐 𝒂𝒏𝒅<𝟔 <𝟒 𝒂𝒏𝒅<𝟓 <𝟒 𝒂𝒏𝒅<𝟕 <𝟑 𝒂𝒏𝒅<𝟕 <𝟒 𝒂𝒏𝒅<𝟖

Final Practice – Identify Angle Relationships Using the diagram, identify the type of angles 1.) <1 𝑎𝑛𝑑<9 5.) <4 𝑎𝑛𝑑<7 2.) <3 𝑎𝑛𝑑<6 6.) <8 𝑎𝑛𝑑<13 3.) <7 𝑎𝑛𝑑<15 4.) <1 𝑎𝑛𝑑<16 7 8 6 5 4 3 2 1 15 16 14 13 12 11 10 9