Tikigaq Geometry Point Hope, AK

Unit: Angles and Transversals Unit 3: This unit Introduces Transversals, and angles based on transversals, including corresponding angles, Same Side Interior Angles, Alternate Exterior and Alternate Interior Angles, and the unique properties of Perpendicular Transversals. 125 2 3 4 X+ 15 7 8 5

Transversal A transversal is a line which cuts across two or more coplanar lines –they may or may not be parallel Transversals create special angle pairs which have properties that we can use to solve their measure of degree Transversal Parallel Lines are indicated by arrows

Corresponding Angles Corresponding Angles: These are angles which occupy corresponding (or matching) positions on two different lines- Angle 1 corresponds with Angle 5 Which angle corresponds with angle 4? Which angle corresponds with angle 2? 1 2 3 4 5 6 7 8

Corresponding Angles on Parallel Lines Corresponding Angles Postulate If a transversal intersects 2 parallel lines, then corresponding angles are congruent If the measure of angle 3 is 75 degrees, what is the measure of angle 2? (Vertical Angles) What is the measure of Angle 7? (Corresponding Angles) What is the measure of Angle 6? What is the measure of Angle 4 (Supplementary Angles)? What is the measure of Angle 8 (corresponding angles)? 1 2 3 4 6 7 8 5

Alternate Interior Angles These angles lie between the two lines, on opposite sides of the transversal Alternate Interior Angles Theorem If a transversal intersects 2 parallel lines, then alternate interior angles are congruent Here, angle 3 and angle 6 are Alternate angles. What is the alternate interior angle that matches up with angle 5? If angle 5 is 130 degrees, what is the measure of angle 4? What is the measure of Angle 6? What is the measure of Angle 3? 1 2 3 4 6 7 8 5

Consecutive Interior Angles, or Same Side Interior Angles If two angles lie between the two lines on the same side of the transversal they are consecutive interior angles, or same-side interior angles Same-Side Interior Angles Theorem If a transversal intersects 2 parallel lines, then same-side interior angles are supplementary Angle 3 and Angle 5 are Same Side Interior Angles If angle 5 is 120 degrees, what is the measure of angle 3? What is the measure of angle 4? What is the measure of angle 6? 1 2 3 4 6 7 8 5

Alternate Exterior Angles If two angles lie outside the two lines, on opposite sides of the transversal, then they are Alternate Exterior Angles Alternate Exterior Angles Theorem If a transversal intersects 2 parallel lines, then Alternate Exterior Angles are congruent Angle 1 and Angle 8 are alternate exterior angles What is the alternate exterior angle for angle 7? If angle 8 measures 140 degrees, what is the measure of angle 1? 1 2 3 4 6 7 8 5

Perpendicular Transversals If a transversal is perpendicular to one of two parallel lines, it is perpendicular to the other parallel line Here, we are given enough information to conclude that line c is perpendicular to line a, because it forms a right (90 degree) angle Because line a is parallel to line b, we can conclude that line c is also perpendicular to line b a b c

Example Find the value of X These are like puzzles: Here, we see that angle 4 is vertical with an angle that is 125 degrees. Therefore, angle 4 is 125 degrees We see that angle 4, and the angle (x+15) are same-side interior angles We know that Same-Side interior angles are supplementary (they add up to 180 degrees) Therefore 125 + X + 15 = 180 Or: 140 + X = 180 Or: X = 40 125 2 3 4 X+ 15 7 8 5

Unit Quiz Use the picture at the right to answer the following questions 1 2 3 4 6 7 8 5 Name a pair of Corresponding Angles Name a pair of Alternate Interior Angles Name a pair of Same Side Interior Angles Name a pair of Alternate Exterior Angles (Yes/No) Are Corresponding Angles congruent? (Yesn/No) are Same Side Interior Angles congruent? If angle 1 measures 130 degrees, what is the measure of angle 8? If angle 2 measures 65 degrees, and angle 6 is (2x-15), what is x? If angle 7 measures 48 degrees, what is the measure of angle 4? If angle 3 measures (4x+8) and angle 6 measures (8x), what is x?

Unit Extra Quiz The measure of Angle 1 is 6x 2 3 4 6 7 8 5 The measure of Angle 1 is 6x The measure of Angle 2 is 2x-20 What is the value of x? How many degrees is the measure of angle 6? What is the measure of angle 5? What type of angle pair are angle 3 and angle 6? What can you conclude about line a and line b? 2 points each, show all work (equations as required) a b