Warm Up 𝑚∠𝐴𝐵𝐶= 𝟖𝟐 𝒐 2.) 𝑚∠𝐴𝐵𝐷= 135 𝑜 . Solve for the 𝑚∠𝐴𝐵𝐶. 1.) Points A,B, and C are collinear. Point B is between A and C. Solve for x and justify each step. 𝐴𝐵=2𝑥+4, 𝐵𝐶=28, and 𝐴𝐶=6𝑥. 2.) 𝑚∠𝐴𝐵𝐷= 135 𝑜 . Solve for the 𝑚∠𝐴𝐵𝐶. 𝑚∠𝐴𝐵𝐶+𝑚∠𝐶𝐵𝐷=𝑚∠𝐴𝐵𝐷 4𝑥+2 + 3𝑥−7 =135 7𝑥−5=135 7𝑥=140 𝑥=20 𝑚∠𝐴𝐵𝐶=4𝑥+2 𝑚∠𝐴𝐵𝐶=4 20 +2 𝑚∠𝐴𝐵𝐶=80+2 𝑚∠𝐴𝐵𝐶= 𝟖𝟐 𝒐 Statements Reasons 1.) 𝐴𝐵=2𝑥+4, 𝐵𝐶=28, and 𝐴𝐶=6𝑥. 1.) Given 2.) 𝐴𝐵+𝐵𝐶=𝐴𝐶 2.) Segment Addition Postulate 3.) 2𝑥+4 + 28 =(6𝑥) 3.) Substitution POE 4.) 2𝑥+32=6𝑥 4.) Simplify 5.) 32=4𝑥 5.) Subtraction POE 6.) 4𝑥=32 6.) Symmetric POE 7.) 𝑥=8 7.) Division POE

Angles and Parallel Lines Mr. Riddle

Parallel Lines When looking at a diagram, parallel lines are shown by arrowheads. Line m is parallel to line p. m p

Transversals A transversal is a line that intersects two or more coplanar lines at different points. t

Corresponding Angles Corresponding Angles – in the diagram, and are corresponding angles. 2 6 t

Alternate Interior Angles Alternate Interior Angles – and in the diagram, and are alternate interior angles. Opposite sides of the transversal and on the inside of the two lines. t 5 4

Alternate Exterior Angles Alternate Exterior Angles – and in the diagram, and are alternate exterior angles. Opposite sides of the transversal and on the outside of the two lines. t 8 1

Same-Side Interior Angles Same-Side Interior Angles- and in the diagram and are consecutive interior angles. They lie between the two lines and on the same side of the transversal. t 7 3

Examples Using the Diagram to the right. Describe the relationships between the angles. 1.) 2.) 3.) 4.) 5.) 6.) Corresponding Consecutive Interior Alternate Exterior Vertical Alternate Interior Linear Pair

Activity 1.) Draw two parallel lines on the graph of your whiteboard. 2.) Draw a transversal that goes through your parallel lines. 3.) Number your angles 1-8 from top right to bottom left. 4.) Measure all 8 of your angles and record their measures.

Activity Based off of the angle measures you got, answer the following questions. Come up with a conclusion for each type of angle relationship. 5.) Corresponding Angles: 6.) Alternate Interior Angles: 7.) Consecutive Interior Angles: 8.) Alternate Exterior Angles:

Corresponding Angles Corresponding Angles Postulate – If 2 parallel lines are cut by a transversal, then the corresponding angles are congruent. In the diagram, . t 1 2

Alternate Interior Angles Alternate Interior Angles Theorem – If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent. In the diagram, . t 4 3

Alternate Exterior Angles Alternate Exterior Angles Theorem – If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent. In the diagram, . t 6 5

Consecutive Interior Angles Consecutive Interior Angles Theorem - If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary. In the diagram, ∠7 and ∠8 are supplementary. t 8 7

Example A: Using Algebra

ANSWERS: 3a: 𝒙=𝟐𝟎 3b: 𝒚=𝟑𝟖

Homework ALEKS #10