* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download NAME: 3.2 Properties of Parallel Lines
Survey
Document related concepts
Integer triangle wikipedia , lookup
Cardinal direction wikipedia , lookup
History of trigonometry wikipedia , lookup
Riemannian connection on a surface wikipedia , lookup
Multilateration wikipedia , lookup
Pythagorean theorem wikipedia , lookup
Perceived visual angle wikipedia , lookup
Line (geometry) wikipedia , lookup
Perspective (graphical) wikipedia , lookup
Rational trigonometry wikipedia , lookup
Trigonometric functions wikipedia , lookup
Compass-and-straightedge construction wikipedia , lookup
Transcript
NAME:___________________ 3.2 Properties of Parallel Lines Corresponding Angles Postulate: Find the degree measure of all the angles. Tell how you got them? What other angle pair relationships are there? Alternate Interior Angles Theorem If a transversal intersects two parallel lines, then Same-Side Interior Angles Theorem: If a transversal intersects two parallel lines, then Alternate Exterior Angles Theorem If a transversal intersects two parallel lines, then Ex 1: Find the measures of all of the angles. Ex 2: Find the measure of each angle indicated. Ex 3: Solve for x. Your try: Summary: ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ 3.2 Practice Problems Directions: Identify all the numbered angles that are congruent to the given angle. JUSTIFY your answer. 2) 1) Directions: Solve for x. 3) 4) 5) 6) Directions: Find the measure of the angle indicated in bold. 8) 7) 9) 10) 11) 12) 13) Solve for x. Opposite sides of the figure are parallel. 14) Solve for x. The top and bottom sides are parallel. Algebra Review Solve: 2 4 Solve: 15 = 2x - 13 Factor: 14 45 Factor: 16 Graph: 56 6 Graaph: 3 4 3.2 APPLICAT TION and EX TENSION DIRE ECTIONS: SOLVE S FOR X. X 1) Opposite side es are paralle el. 2) O 3) New York City y’s streets arre laid out in a grid so mo ost of the st reets all line e up parallel a and perpendiicular to each h othe er. However, there are a few streets that go diag gonally througgh town. The picture below is a repre esentation of f BROADWAY in NYC. N It’s a transversal t to o the three parallel stree ets. Use thiis informatio on to answer the following g questtions. a) If ∠ 42° and W.. 62nd and W.. 61st are parrallel find the e following: m∠ m∠ m∠ m m∠ m∠ m∠ m b) If ∠ m∠ m∠ 42° and W. 62nd is also parallel to W 60th find t he following:: m∠ c) What kind k of angle es are ∠ , ∠ , ∠ ? d) If the lines are all parallel p then what should be true abo ut all three o of the angles? Is I it true? 4) Spiderman is slinging is way all over NYC. He starts on one building and is going to sling across to the building opposite which is parallel to the building he is on. He knows that the angle formed between his webbing and the building (on the bottom side) is 37°. Draw a picture and find the angle that the webbing and building (on the bottom side form. 5) Write a two-column proof. Given: ∥ , ∠1 ≅ ∠4 Prove: ∠2 ≅ ∠3