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Objectives: Measure and Classify Angles Describe Angle Pair Relationships Classify Angle Pairs made by Parallel Lines cut by a Transversal Describe Angle Pair Relationships within Parallel Lines. Geometry Review Angles and Parallel Lines. Part 1: Angles.

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Objectives:Measure and Classify AnglesDescribe Angle Pair RelationshipsClassify Angle Pairs made by Parallel Lines cut by a TransversalDescribe Angle Pair Relationships within Parallel Lines Geometry Review Angles and Parallel Lines

Part 1: Angles • An angle consists of two different rays (sides) that share a common endpoint (vertex). Vertex Sides This angle can be called: Angle ABC, <ABC, <CBA OR it can be named by the vertex like so: <B

Types of Angles Go to the following website to learn about the different types of angles. Don’t forget to press the play button on top of the picture to see the animation. Use the diagram to find the measure of the indicated angle. Then classify each angle as either acute, right, obtuse, or straight. • KHJ • GHK • GHJ • GHL http://www.mathsisfun.com/angles.html

5. What is the measure of DOZ?… How did you get to your answer?

Angle Addition Postulate If P is in the interior of RST, then mRST = mRSP + mPST.

6. Given that mLKN = 151°, find mLKM and mMKN.

Congruent Angles • Two angles are congruent angles if they have the same measure.

Angle Bisector An angle bisector is a ray that divides an angle into two congruent angles.

7. Ray BD bisects <ABC. Solve for x. A D B C

8. In a diagram, YW bisects XYZ. mXYW = ° and m ZYW= (-18m)°. Find mXYW. Hint: Draw the picture Hint: Angle may not be drawn to scale

C Comes Before S…Complementary Angles Sum to 90 DegreesSupplementary Angles Sum to 180

Linear Pairs of Angles • Two adjacent angles form a linear pair if their noncommon sides are opposite rays. • The angles in a linear pair are supplementary.

Vertical Angles • Two nonadjacent angles are vertical angles if their sides form two pairs of opposite rays. • Vertical angles are formed by two intersecting lines.

S U • Name a pair of complementary angles. • Name a pair of supplementary angles. • Name a linear pair. • Name a pair of vertical angles. • Name a pair of congruent angles. Y T V X W

Part 2: Parallel Lines What would you call two lines which do not intersect? Answer: Parallel Lines A solid arrow placed on two lines of a diagram indicate the lines are parallel. Exterior Interior The symbol || is used to indicate parallel lines. Exterior AB || CD

A slash through the parallel symbol || indicates the lines are not parallel. AB || CD

Parallel lines Non-Parallel lines transversal transversal Transversal Definition: A line, ray, or segment that intersects 2 or more COPLANAR lines, rays, or segments. Exterior Exterior Interior Interior Exterior Exterior

Transversal – A transversal is a line which intersects two or more lines in a plane. The intersected lines do not have to be parallel. Lines j, k, and m are intersected by line t. Therefore, line t is a transversal of lines j, k, and m.

exterior interior exterior INTERIOR –The space INSIDE the 2 lines In the diagram below: Angles 1, 2, 7 and 8 are exterior angles. Angles 3, 4, 5, and 6 are on the interior. EXTERIOR -The space OUTSIDE the 2 lines Exterior 1 2 3 4 Interior 5 6 7 8 Exterior

1 2 3 4 6 5 7 8 When two parallel lines are cut by a transversal special angle relationships form. ♥Alternate Interior Angles are CONGRUENT ♥Alternate Exterior Angles are CONGRUENT ♥Same Side Interior Angles are SUPPLEMENTARY ♥Same Side Exterior Angles are SUPPLEMENTARY Exterior Interior Exterior

Corresponding Angles Corresponding Angles: Two angles that occupy corresponding positions. 2 6, 1 5,3 7,4 8 Exterior 1 2 3 4 Interior 5 6 7 8 Exterior

L Line L G Line M P A B Line N Q D E F Corresponding Angles When two parallel lines are cut by a transversal, pairs of corresponding angles are formed. ÐGPB = ÐPQE ÐGPA = ÐPQD ÐBPQ = ÐEQF ÐAPQ = ÐDQF Four pairs of corresponding angles are formed. Corresponding pairs of angles are congruent.

Lines l and m are parallel. l||m. 14. Name all pairs of corresponding angles. 15. Determine all the missing angle measures. 42° a ° c° b° l d° e° g° f° m

L Line L G Line M P A B Line N Q D E F Same Side Interior/Exterior Angles Same Side Interior Angles: Two angles that lie between parallel lines on the same sides of the transversal. Same Side Exterior Angles: Two angles that lie outside parallel lines on the same sides of the transversal. ÐAPQ + ÐDQP = 1800 ÐBPQ + ÐEQP = 1800 Exterior 600 1200 Same Side Interior or Same Side Exterior angles are supplementary. Interior 1200 600 Exterior

L Line L G Line M P A B Line N Q D E F Alternate Interior/Exterior Angles Alternate Interior Angles: Two angles that lie between parallel lines on opposite sides of the transversal (but not a linear pair). Alternate Exterior Angles: Two angles that lie outside parallel lines on opposite sides of the transversal. ÐBPQ = ÐDQP ÐAPQ = ÐEQP Two pairs of alternate angles are formed. Pairs of alternate angles are congruent.

Lines l and m are parallel. l||m16. Name all pairs of alternate interior angles. 17. Name all pairs of alternate exterior angles. 18. Determine all the missing angle measures. 81° a ° c° b° l d° e° g° f° m

Line L G Line M P A B 500 Line L G 1300 Line M Line N A P B Q E D Line L G F Line N Q D E Line M P A B F Line N Q E D F Make sure you are in slide show view to do this test. Name the pairs of the following angles formed by a transversal. Test Yourself Corresponding angles Alternate angles Interior angles

19) Find the missing angles. 70 ° 70 ° b° Hint: The 3 angles in a triangle sum to 180°. d ° 65 °

20) Find the missing angles. 45 ° 50 ° b° Hint: The 3 angles in a triangle sum to 180°. d ° 75 °

In the figure a || b. 21.Name the angles congruent to 3. 22.Name all the angles supplementary to 6. 23.If m1 = 105° what is m3? 24.If m5 = 120° what is m2?

25. Final Exercise 40° Find all the missing angle measures, and name the postulate or theorem that gives us permission to make our statements. 60°