* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download transversals and angle pair properties 14
Survey
Document related concepts
Riemannian connection on a surface wikipedia , lookup
Technical drawing wikipedia , lookup
Perspective (graphical) wikipedia , lookup
Rotation formalisms in three dimensions wikipedia , lookup
Integer triangle wikipedia , lookup
Pythagorean theorem wikipedia , lookup
Perceived visual angle wikipedia , lookup
History of trigonometry wikipedia , lookup
Line (geometry) wikipedia , lookup
Rational trigonometry wikipedia , lookup
Compass-and-straightedge construction wikipedia , lookup
Multilateration wikipedia , lookup
Trigonometric functions wikipedia , lookup
Transcript
transversals and angle pair properties 1415.notebook Geo opener Learning Targets October 17, 2014 101714 transversals and special angle pair theorems Use a geometry term to describe the special angle pairs that are formed 1) <1 and <4 Vertical Angles 2) <3 and <4 Linear Pair 3) <1 and <8 Alt. Ext. Angles 4) <5 and <4 Alt. Int. Angles 5) <1 and <5 Corresponding Angles 6) <6 and <4 Consec. Int. Angles Word Bank transversals and angle pair properties 1415.notebook October 17, 2014 transversals and angle pair properties 1415.notebook October 17, 2014 line a is parallel to line b. Line c is a transversal 12 0o 60 o What do you notice about the following types of angles a 120 120o 60o o021 o 120o 60o b c Vertical Angles Alt. Int. Angles Alt. Ext. Angles Linear Pair Corresponding Angles Consec. Int. Angles line a is Not parallel to line b. Line c is a transversal What do you notice about the following types of angles120 120o 60 60oo a o b 60o o Vertical Angles Linear Pair 021 c Alt. Int. Angles Alt. Ext. Angles Corresponding Angles Consec. Int. Angles transversals and angle pair properties 1415.notebook October 17, 2014 Corresponding Angles Postulate by construction Boxes Corr. are iff the 2 lines cut by the transversal are //. Alternate Interior Angles Theorem Alternate interior angles are congruent if and only if the two lines cut by the transversal are parallel. A.I.A are iff the 2 lines cut by the transversal are //. If a//b, then a 2 1 4 3 5 b 6 8 7 c Boxes shorthand??? shorthand??? Corresponding angles are congruent if and only if the two lines cut by the transversal are parallel. proof? AIA are transversals and angle pair properties 1415.notebook October 17, 2014 Alternate Exterior Angles Theorem A.E.A a boxes shorthand??? Alternate Exterior angles are congruent if and only if the two lines cut by the transversal are parallel. boxes Consecutive interior angles are supplementary if and only if the two lines cut by the transversal are parallel. shorthand??? Consecutive Interior Angles Theorem C.I.A ar transversals and angle pair properties 1415.notebook m< 1 = 500 October 17, 2014 Find the measure of the rest of the angles m< 2 = 1 2 4 3 m< 3 = m< 4 = 56 8 7 m< 5 = m<6 = m< 7 = m< 8 = In the figure at the right p is parallel to q. Find the measure of each angle. <1=78, <2=47 1. m<3 4 6 2. m<4 3. m<5 3 5 4. m<6 5. m<7 1 9 q 6. m<8 7. m<9 8. m<10 p 10 2 8 7