8-3 Do Now Draw each figure. 1. line segment 2. line 3. ray 4. plane Course 2 8-3 EQ: How do I identify parallel, perpendicular, and angles formed by a transversal? Do Now Draw each figure. 1. line segment 2. line 3. ray 4. plane HWK: Wbk P 70

M7A2a Given a problem, define a variable, write an equation, solve the equation and interpret the solution.

Insert Lesson Title Here Course 2 Angles Insert Lesson Title Here Vocabulary Review Angle – Vertex - right angle - angle that that measures. The symbol Γ indicates a right angle.

acute angle - is an angle that measures obtuse angle - an angle that measures straight angle - is an angle that measures complementary angles – the sum of the measures of two angles is ?0 supplementary angles – the sum of the measures of two angles is ?°

New Vocabulary

perpendicular lines - angles formed by two intersecting lines are equal to 90° parallel lines - lines in the same plane do not intersect at all adjacent angles – angles that have a common vertex and a common side, but no common interior points.

vertical angles - opposite angles formed by two intersecting lines Transversal - a line that intersects two or more lines corresponding angles - are angles on the same side of the transversal and are both above or both below the parallel lines

Course 2 8-3 Angles A C B 1 Vertex An angle is formed by two rays with a common endpoint. The two rays are the sides of the angle. The common endpoint is the vertex. Angles are measured in degrees (°).

8-3 Angles An angle’s measure determines the type of angle it is. Course 2 8-3 Angles An angle’s measure determines the type of angle it is. A right angle is an angle that that measures exactly 90°. The symbol indicates a right angle. An acute angle is an angle that measures less than 90°. An obtuse angle is an angle that measures more than 90° but less than180°. A straight angle is an angle that measures 180°.

Additional Example 1: Classifying Angles Course 2 8-3 Angles Additional Example 1: Classifying Angles Tell whether each angle is acute, right, obtuse or straight. A. B. obtuse angle acute angle

Insert Lesson Title Here Course 2 8-3 Angles Insert Lesson Title Here Check It Out: Example 1 Tell whether each angle is acute, right, obtuse, or straight. B. A. straight angle acute angle

8-3 Angles Reading Math You can name this angle ABC, CBA, B, or 1. Course 2 8-3 Angles You can name this angle ABC, CBA, B, or 1. Reading Math A • B • • C 1

8-3 Angles If the sum of the measures of two angles is Course 2 8-3 Angles If the sum of the measures of two angles is 90°, then the angles are complementary angles. If the sum of the measures of two angles is 180°, then the angles are supplementary angles.

Course 2 8-3 Angles Use the diagram to tell whether the angles are complementary, supplementary, or neither. OMP and PMQ O N P Q R M complementary.

Course 2 8-3 Angles If the angle you are measuring appears obtuse, then it measure is greater than 90°. If the angle is acute, its measure is less than 90°. Reading Math

Course 2 8-3 Angles Use the diagram to tell whether the angles are complementary, supplementary, or neither. O N P Q R M NMO and OMR

Course 2 8-3 Angles Use the diagram to tell whether the angles are complementary, supplementary, or neither. O N P Q R M PMQ and QMR

Course 2 8-3 Angles Use the diagram to tell whether the angles are complementary, supplementary, or neither. BAC and CAF C B D E F A

Course 2 8-3 Angles Use the diagram to tell whether the angles are complementary, supplementary, or neither. C B D E F A CAD and EAF

Course 2 8-3 Angles Use the diagram to tell whether the angles are complementary, supplementary, or neither. C B D E F A BAC and EAF

Course 2 8-3 Angles Angles A and B are complementary. If mA is 56°, what is the mB? What is the supplement of A?

Course 2 8-3 Angles Angles P and Q are supplementary. If mP is 32°, what is the mQ? What is the complement of P?

Course 2 8-3 Angle Relationships The symbol means “is parallel to.” The symbol means “is perpendicular to.” Reading Math

Course 2 8-3 Angle Relationships Tell whether the lines appear parallel or perpendicular. UV and YV The lines appear to intersect to form right angles. UV  YV

Course 2 8-3 Angle Relationships Tell whether the lines appear parallel or perpendicular. XY and WZ The lines are in the same plane and do not intersect. XY || WZ

Course 2 8-3 Angle Relationships Tell whether the lines appear parallel or perpendicular. WX and XU WX  XU The lines appear to intersect to form right angles.

Course 2 8-3 Angle Relationships Tell whether the lines appear parallel or perpendicular. WX and ZY The lines are in the same plane and do not intersect. WX || ZY

Course 2 8-3 Angle Relationships Adjacent angles have a common vertex and a common side, but no common interior points. Angles 2 and 3 in the diagram are adjacent. Adjacent angles formed by two intersecting lines are supplementary

Vertical angles are the opposite angles formed by two intersecting lines. When two lines intersect, two pairs of vertical angles are formed. Vertical angles have the same measure, so they are congruent.

Course 2 8-3 Angle Relationships Angles with the same number of tick marks are congruent. The tick marks are placed in the arcs drawn inside the angles.

Course 2 8-3 Angle Relationships A transversal is a line that intersects two or more lines. Line t is a transversal. When the lines that are intersected are parallel, four pairs of corresponding angles are formed.

Corresponding angles are on the same side of the transversal and are both above or both below the parallel lines. Angles 1 and 5 are corresponding angles. Corresponding angles are congruent.

8-3 Angle Relationships Line n line p. Find the measure of the angles. Course 2 8-3 Angle Relationships Line n line p. Find the measure of the angles.

8-3 Angle Relationships 45° 4 5 6 2 3 7 n p Course 2 8-3 Angle Relationships Line n line p. Find the measure of the angles. 45° 4 5 6 2 3 135° 7 n p

Insert Lesson Title Here Course 2 8-3 Angles TOTD Insert Lesson Title Here Tell whether each angle is acute, right, obtuse, or straight. 1. straight 2. obtuse

Insert Lesson Title Here Course 2 8-3 Angles TOTD Insert Lesson Title Here Use the diagram to tell whether the angles are complementary, supplementary, or neither. 3. AZB and BZC neither 4. BZC and CZD complementary 5. Angles M and N are supplementary. If M is 117°, what is mN? 63°

Angle Relationships TOTD Insert Lesson Title Here Course 2 8-3 Angle Relationships TOTD Insert Lesson Title Here Tell whether the lines appear parallel, perpendicular, or skew. 1. AB and CD 2. EF and FH parallel perpendicular