3-1 Parallel Lines and Transversals

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Presentation transcript:

3-1 Parallel Lines and Transversals

CCSS Content Standards G.CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. Mathematical Practices 1 Make sense of problems and persevere in solving them. 3 Construct viable arguments and critique the reasoning of others.

Then/Now You used angle and line segment relationships to prove theorems. Identify relationships between two lines or two planes. Name angle pairs formed by parallel lines and transversals.

Vocabulary parallel lines skew lines parallel planes transversal interior angles exterior angles consecutive interior angles alternate interior angles alternate exterior angles corresponding angles

Concept

Vocabulary transversal: a line that intersects two or more coplanar lines at two different points

Example 1 A. Name all segments parallel to BC. Answer: AD, EH, FG

Example 1 B. Name a segment skew to EH. Answer: AB, CD, BG, or CF

Example 1 C. Name a plane parallel to plane ABG. Answer: plane CDE

Example 1a A. Name a plane that is parallel to plane RST. A. plane WTZ B. plane SYZ C. plane WXY D. plane QRX

Example 1b B. Name a segment that intersects YZ. A. XY B. WX C. QW D. RS

Example 1c C. Name a segment that is parallel to RX. A. ZW B. TZ C. QR D. ST

Concept

Vocabulary Interior angles Example:

Vocabulary Exterior angles Example:

Vocabulary Consecutive interior angles Example:

Vocabulary Alternate interior angles Example:

Vocabulary Alternate exterior angles Example:

Vocabulary Corresponding angles Example:

Example 2 A. Classify the relationship between 2 and 6 as alternate interior, alternate exterior, corresponding, or consecutive interior angles. Answer: corresponding

Example 2 B. Classify the relationship between 1 and 7 as alternate interior, alternate exterior, corresponding, or consecutive interior angles. Answer: alternate exterior

Example 2 C. Classify the relationship between 3 and 8 as alternate interior, alternate exterior, corresponding, or consecutive interior angles. Answer: consecutive interior

Example 2 D. Classify the relationship between 3 and 5 as alternate interior, alternate exterior, corresponding, or consecutive interior angles. Answer: alternate interior

Example 2a A. Classify the relationship between 4 and 5. A. alternate interior B. alternate exterior C. corresponding D. consecutive interior

Example 2b B. Classify the relationship between 7 and 9. A. alternate interior B. alternate exterior C. corresponding D. consecutive interior

Example 2c C. Classify the relationship between 4 and 7. A. alternate interior B. alternate exterior C. corresponding D. consecutive interior

Example 2d D. Classify the relationship between 2 and 11. A. alternate interior B. alternate exterior C. corresponding D. consecutive interior

Example 3 A. BUS STATION The driveways at a bus station are shown. Identify the transversal connecting 1 and 2. Then classify the relationship between the pair of angles. Answer: The transversal connecting 1 and 2 is line v. These are corresponding angles.

Example 3 B. BUS STATION The driveways at a bus station are shown. Identify the transversal connecting 2 and 3. Then classify the relationship between the pair of angles. Answer: The transversal connecting 2 and 3 is line v. These are alternate interior angles.

Example 3 C. BUS STATION The driveways at a bus station are shown. Identify the transversal connecting 4 and 5. Then classify the relationship between the pair of angles. Answer: The transversal connecting 4 and 5 is line y. These are consecutive interior angles.