* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download chapter 2 - pmaguire
Survey
Document related concepts
Rotation formalisms in three dimensions wikipedia , lookup
Pythagorean theorem wikipedia , lookup
Integer triangle wikipedia , lookup
Perspective (graphical) wikipedia , lookup
History of trigonometry wikipedia , lookup
Geometrization conjecture wikipedia , lookup
Line (geometry) wikipedia , lookup
Multilateration wikipedia , lookup
Rational trigonometry wikipedia , lookup
Poincaré conjecture wikipedia , lookup
Perceived visual angle wikipedia , lookup
Trigonometric functions wikipedia , lookup
Transcript
Geometry Chapter 2 LESSON 2.5 ANGLE RELATIONSHIPS Linear Pair Conjecture C-1 If two angles form a linear pair, then the measure of the angles add up to 180 degrees. . Vertical Angles Conjecture C-2 If two angles are vertical angles, then they have equal measures (are congruent). 3 2 4 1 Measure of angle 1 equals the measure of angle ______. While the Measure of angle 2 equals the measure of angle ______. Putting C-1 and C-2 Together Example Problems: Solve for the missing variables. 130 50 x y 130 46 48 b 86 a cd 86 46 48 z 50 Solution: x + 130 = 180 (C-1) -130 -130 x = 50 **Use C-2 to solve for y and z. Solution: 48 + a + 46 = 180 (Conjecture???) a + 94 = 180 - 94 - 94 a = 86 **Use C-2 to solve for b,c,and d. CHAPTER 2 LESSON 2.6 SPECIAL ANGLES ON PARALLEL LINES PARALLEL LINES CONJECTURE C-3 If two parallel lines are cut by a transversal, then corresponding angles are… CONGRUENT, alternate interior angles are… CONGRUENT, and alternate exterior angles are… CONGRUENT. KEY: Lines must be proven parallel. Corresponding Angles Conjecture C-3a (CA Conjecture) If two parallel lines are cut by a transversal, then corresponding angles are ____________ CONGRUENT. 1 2 Angle 1 is congruent to angle 2. They are corresponding angles. 52 degrees Therefore, if angle 1 is 52 degrees, then angle 2 is __________. Alternate Interior Angles Conjecture C-3b (AIA Conjecture) If two parallel lines are cut by a transversal, then CONGRUENT alternate interior angles are _____________. a 3 d 4 e f Angle 3 is congruent to angle 4. They are alternate interior angles. b c Use the AIA conjecture to determine which angle is congruent to angle c??? Answer: angle d Alternate Exterior Angles Conjecture C-3c (AEA Conjecture) If two parallel lines are cut by a transversal, then alternate exterior angles are _____________. CONGRUENT A B C D EF G H According to the AEA conjecture, list all congruent angles. Answer: Angle A and Angle H Angle B and Angle G CONVERSE OF THE PARALLEL LINES CONJECTURE C-4 If two lines are cut by a transversal to form pairs of congruent corresponding angles, congruent alternate interior angles, or congruent alternate exterior angles, then the lines are……………………………. HOMEWORK Page 124; #1-6 Page 131; #1-7, 9,10, 14-16