Homework Review CCGPS Analytic Geometry Day 3 11314

Homework Review

CCGPS Analytic Geometry Day 3 (1/13/14) UNIT QUESTION: How do I prove geometric theorems involving lines, angles, triangles and parallelograms? Standards: MCC 9 -12. G. SRT. 1 -5, MCC 9 -12. A. CO. 6 -13 Today’s Question: Which angles are congruent to each other when parallel lines are cut by a transversal? Standard: MCC 9 -12. A. CO. 9

Parallel Lines and Transversals

Parallel Lines – Two lines are parallel if and only if they are in the same plane and do not intersect. B A C D AB CD

Parallel Planes – Planes that do not intersect.

Skew Lines – two lines that are NOT in the same plane and do NOT intersect

Ex 1: Name all the parts of the prism shown below. Assume segments that look parallel are parallel. 1. A plane parallel to F E plane AFE. Plane BGD G A D 2. All segments that intersect GB. AB, FG, DG, BC C B 3. All segments parallel to FE. GD, BC 4. All segments skew to ED. BG, FA, BC

Transversal – A line, line segment, or ray that intersects two or more lines at different points. a b t Line t is a transversal.

Special Angles 1 2 3 4 6 5 7 8 Interior Angles – lie between the two lines ( 3, 4, 5, and 6) Alternate Interior Angles – are on opposite sides of the transversal. ( 3 & 6 AND 4 and 5) Consecutive Interior Angles – are on the same side of the transversal. ( 3 & 5 AND 4 & 6)

More Special Angles Exterior Angles – lie outside the two lines ( 1, 2, 7, and 8) 1 2 34 5 68 7 Alternate Exterior Angles – are on opposite sides of the transversal ( 1& 8 AND 2 & 7)

Ex. 2: Identify each pair of angles as alternate interior, alternate exterior, consecutive interior, or vertical. a. 1 and 2 1 6 7 3 4 8 5 2 Alt. Ext. Angles b. 6 and 7 Vertical Angles c. 3 and 4 Alt. Int. Angles d. 3 and 8 Consec. Int. Angles

Alternate Interior Angles Theorem If two parallel lines are cut by a transversal, then each pair of alternate interior angles are congruent. 1 87 2 6 3 5 4 2 6 3 7

Alternate Exterior Angles Theorem If two parallel lines are cut by a transversal, then each pair of alternate exterior angles are congruent. 1 87 2 6 3 5 4 1 5 4 8

Consecutive Interior Angles Theorem If two parallel lines are cut by a transversal, then each pair of consecutive interior angles are supplementary. 1 87 2 6 3 5 4 m 2 + m 3 = 180° m 6 + m 7 = 180°

Ex. 3 In the figure, p q. If m 5 = 28°, find the measure of each angle. 1 2 34 5 68 7 a. m 8 = 28° q p b. m 1 = 28° c. m 2 = 152° d. m 3 = 152° e. m 4 = 28°

Ex. 4 In the figure, s t. Find the m CBG. t A S D 3 x -5 E G B 4 x -29 C Step 1: Solve for x. 3 x – 5 = 4 x - 29 -5 = x - 29 24 = x F Step 2: m CBG = m ABE = 3 x -5. 3 x-5 = 3(24) – 5 = 72 -5 = 67°

Ex: 5 Identify each pair of angles as: alt. interior, alt. exterior, consecutive interior, or vertical. 16 1 15 2 3 4 10 11 9 12 14 5 13 6 8 7

Ex: 6 Identify each pair of angles as: alt. interior, alt. exterior, consecutive interior, or vertical. 16 1 15 2 3 4 10 11 9 12 14 5 13 6 8 7

Ex: 7 Identify each pair of angles as: alt. interior, alt. exterior, consecutive interior, or vertical. 16 1 15 2 3 4 10 11 9 12 14 5 13 6 8 7

Ex: 8 Identify each pair of angles as: alt. interior, alt. exterior, consecutive interior, or vertical. 16 1 15 2 3 4 10 11 9 12 14 5 13 6 8 7

Ex: 9 Identify each pair of angles as: alt. interior, alt. exterior, consecutive interior, or vertical. 16 1 15 2 3 4 10 11 9 12 14 5 13 6 8 7

Ex: 10 Identify each pair of angles as: alt. interior, alt. exterior, consecutive interior, or vertical. 16 1 15 2 3 4 10 11 9 12 14 5 13 6 8 7