Angle Interior Any points that lie inside the rays of an angle. G B C

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Presentation transcript:

Angle Interior Any points that lie inside the rays of an angle. G B C J H Examples: Point B is in the interior of ÐGHC Point D is in the interior of ÐGHJ and ÐCHJ Point A is NOT in the interior of ÐGHJ B C D A

Classifying Angles Acute Obtuse Right Straight An angle that measures between 0 and 90 degrees. Example: ÐABC is an acute angle. mÐABC = 30. A B C 30° Obtuse An angle that measures between 90 and 180 degrees. Example: ÐDEF is an obtuse angle. mÐDEF = 110. D E F 110° Right An angle that measures exactly 90 degrees. Example: ÐGHJ is a right angle. mÐGHJ = 90. G H J 90° Straight An angle that measures exactly 180 degrees. Example: ÐKLM is a straight angle. mÐKLM = 180. K L M 180° A right angle in a diagram is denoted by a square in the corner of the angle.

Classifying Angles An angle that measures between 0 and 90 degrees. Example: ÐABC is an acute angle. mÐABC = 30. A B C 30° An angle that measures between 90 and 180 degrees. Example: ÐDEF is an obtuse angle. mÐDEF = 110. D E F 110° An angle that measures exactly 90 degrees. Example: ÐGHJ is a right angle. mÐGHJ = 90. G H J 90° An angle that measures exactly 180 degrees. Example: ÐKLM is a straight angle. mÐKLM = 180. K L M 180° A right angle in a diagram is denoted by a square in the corner of the angle.

Congruent Angles Congruent Angles – angles that have equal measures. Recall the Definition of Congruent: Figures that are the same shape and size. Congruent Angles – angles that have equal measures. Notation: ÐMAT @ ÐZIP M A T Z I P 120° mÐMAT = mÐZIP

Adjacent Angles C B T A ÐCAB and ÐBAT are adjacent angles. Two angles that… 1) Share a side. 2) Share their vertex. 3) Do not overlap (share any interior points). C T B A ÐCAB and ÐBAT are adjacent angles. ÐCAT and ÐBAT are NOT adjacent because they share interior points (overlap).

Angle Bisector a ray that divides an angle into two congruent adjacent angles. WY is the angle bisector of ÐXWZ. and therefore, ÐXWY @ ÐYWZ Y X 60° Z W

Complementary & Adjacent Angles Complementary Angles two angles whose measures sum to 90°. 35° 55° 20° 70° Complementary Angles Complementary & Adjacent Angles

Supplementary & Adjacent Angles Supplementary Angles two angles whose measures sum to 180°. 110° 70° 125° 55° Supplementary Angles Supplementary & Adjacent Angles

Linear Pair = A Pair of Angles that forms a Line. two supplementary, adjacent angles. 120° 60° Linear Pair = A Pair of Angles that forms a Line.

Vertical Angles – always congruent! When two lines intersect, they form two pairs of vertical angles. The vertical angle pairs are the non-adjacent angles. 1 2 3 4 Ð1 and Ð2 are vertical angles. Ð3 and Ð4 are vertical angles.