Geometry Chapter 2 LESSON 2 5 ANGLE RELATIONSHIPS

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Geometry Chapter 2 LESSON 2. 5 ANGLE RELATIONSHIPS

Geometry Chapter 2 LESSON 2. 5 ANGLE RELATIONSHIPS

Linear Pair Conjecture C-1 If two angles form a linear pair, then the measure

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 v. If two angles are vertical angles, then they have

Vertical Angles Conjecture C-2 v. 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 v. Example Problems: Solve for the missing variables. x

Putting C-1 and C-2 Together v. Example Problems: Solve for the missing variables. x b a cd y z Solution: x + 130 = 180 (C-1) -130 x = 50 **Use C-2 to solve for y and z. Solution: 48 + a + 46 = 180 (Conjecture? ? ? ) a + 94 = 180 - 94 a = 86 **Use C-2 to solve for b, c, and d.

CHAPTER 2 LESSON 2. 6 SPECIAL ANGLES ON PARALLEL LINES

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

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. ØKEY: Lines must be proven parallel.

Corresponding Angles Conjecture C-3 a (CA Conjecture) If two parallel lines are cut by

Corresponding Angles Conjecture C-3 a (CA Conjecture) If two parallel lines are cut by a transversal, then corresponding angles are ______ CONGRUENT. 1 2 ØAngle 1 is congruent to angle 2. They are corresponding angles. 52 degrees ØTherefore, if angle 1 is 52 degrees, then angle 2 is _____.

Alternate Interior Angles Conjecture C-3 b (AIA Conjecture) If two parallel lines are cut

Alternate Interior Angles Conjecture C-3 b (AIA Conjecture) If two parallel lines are cut by a transversal, then CONGRUENT alternate interior angles are _______. a 3 d 4 e f ØAngle 3 is congruent to angle 4. They are alternate interior angles. b c ØUse the AIA conjecture to determine which angle is congruent to angle c? ? ? Answer: angle d

Alternate Exterior Angles Conjecture C-3 c (AEA Conjecture) If two parallel lines are cut

Alternate Exterior Angles Conjecture C-3 c (AEA Conjecture) If two parallel lines are cut by a transversal, then alternate exterior angles are _______. CONGRUENT A B C D EF G H ØAccording 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

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

HOMEWORK Page 124; #1 -6 Page 131; #1 -7, 9, 10, 14 -16

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