Types of Angles Term Acute Angle Picture and Definition An angle whose measure is LESS than 90o. Term Picture and Definition An angle whose measure is 90o. If two angles from a right angle, they are COMPLIMENTARY. Right Angle (Complimentary) Obtuse Angle An angle whose measure is GREATER THAN 90O. The measure of a line is 180o. If two angles form a line, they are SUPPLEMENTARY. Line (Supplementary) Angle Relationships Name Vertical Angles Picture and Definition Vertical angles are CONGRUENT. (Congruent) Adjacent Angles or Linear Pair Adjacent angles are SUPPLEMENTARY. They are also called a LINEAR PAIR. (Supplementary) Examples Identify the 4 pairs of vertical angles. 1.<1 & <4 2.<2 & <3 3.<7 & <6 4.<5 & <8 x = 115O y = 65O z = 115O Parallel Lines cut by a TRANSVERSAL Using the diagram on the left, identify the following information. Identify the acute angles: 1, 4, 5, 8 Identify the obtuse angles: 2, 3, 6, 7 Identify the pairs of vertical angles: 1&4, 2&3, 5&8, 6&7 Identify the linear pairs: 1&2, 3&4, 5&6, 7&8 π β₯ π; π ππ π π»πΉπ¨π΅πΊπ½π¬πΉπΊπ¨π³ Angle Relationships in Parallel Lines Name Corresponding Angles Picture and Definition Corresponding angles are CONGRUENT. Examples Identify the following: a = 145 b = 145 x = 35 y = 35 (CONGRUENT) π ≅ π; π ≅ π; π ≅ π; π ≅ π Alternate Interior Angles Alternate interior angles are INSIDE the parallel lines and OPPOSITE of the transversal. The angles are CONGRUENT. (CONGRUENT) < π ≅< π; < π ≅< π Identify the following: x = 98 y = 82 z = 82 Alternate Exterior Angles (CONGRUENT) Same Side Interior Angles (SUPPLEMENTARY) Alternate exterior angles are OUTSIDE the parallel lines and OPPOSITE the transversal. The angles are CONGRUENT. < π+< π = πππ; < π+< π = πππ (SUPPLEMENTARY) Yes or No Explain your answer: The numbers 130o and 40o do not form a linear pair so the streets < π ≅< π; < π ≅< π cannot be parallel. Same side interior angles are INSIDE the parallel lines and on Identify the following: the SAME SIDE of the transversal. The angles are SUPPLEMENTARY Same Side Exterior Angles Julio wants to know if Franklin Way and Chavez Ave are parallel. Same side exterior angles are OUTSIDE the parallel lines and on the SAME SIDE of the transversal. The angles are SUPPLEMENTARY < π+< π = πππ x = 130; y = 50 If angle 1 = 100o, find the measure of angle 7. Use the diagram on the left. m<7 = 80o Types of Angles Term Acute Angle Picture and Definition An angle whose measure is ____________________. Term Picture and Definition An angle whose measure is ____o. If two angles from a right angle, they are ___________________________. Right Angle (Complimentary) Obtuse Angle An angle whose measure is _____________________________. The measure of a line is ______o. If two angles form a line, they are _________________________________. Line (Supplementary) Angle Relationships Name Vertical Angles Picture and Definition Vertical angles are ________________________. (Congruent) Adjacent Angles or Linear Pair Adjacent angles are _______________________. They are also called a ___________________________. (Supplementary) Examples Identify the 4 pairs of vertical angles. 1.________ 2.________ 3.________ 4.________ x = ______ y = ______ z = ______ Parallel Lines cut by a TRANSVERSAL Using the diagram on the left, identify the following information. Identify the acute angles: ____________________________________ Identify the obtuse angles: ____________________________________ Identify the pairs of vertical angles: ____________________________________________ Identify the linear pairs: ____________________________________ π β₯ π; π ππ π __________________ Angle Relationships in Parallel Lines Name Corresponding Angles Picture and Definition Corresponding angles are ___________________________. Examples Identify the following: a = __________ b = __________ x = __________ y = __________ (_________) π ≅ _____; π ≅ _____; π ≅ ______; π ≅ _____ Alternate Interior Angles Alternate interior angles are _____________ the parallel lines and _______________ of the transversal. The angles are ________________. (_________) < π ≅< ______; < π ≅< ______ Identify the following: x = _________ y = _________ z = _________ Alternate Exterior Angles (__________) Alternate exterior angles are ___________________ the parallel lines and ___________________ the transversal. The angles are ______________________. (____________) Yes or No Explain your answer: < _____ ≅< π; < π ≅< _____ Same Side Interior Angles Julio wants to know if Franklin Way and Chavez Ave are parallel. Same side interior angles are _________________ the parallel lines and on the ______________ of the transversal. The angles are ______________________. Identify the following: < π+< ______ = πππ; < π+< π = ______ Same Side Exterior Angles (____________) Same side exterior angles are ________________ the parallel lines and on the _________________ of the transversal. The angles are ____________________________. < π+< _______ = _______ x = ________; y =_________ If angle 1 = 100o, find the measure of angle 7. Use the diagram on the left. m<7 = _________o
