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8-2 Classifying Angles Warm Up Problem of the Day Lesson Presentation Course 2 8-2 Classifying Angles Warm Up 1. What percent of the model is shaded? 71% 2. Find the value of 52 + 53. 150 3. What is the percent of change if 20 is increased to 25? 25% 4. On a scale drawing of a tree with a scale of 1 cm = 0.9 m, the height of the tree is 1.2 cm. What is the actual height of the tree? 1.08 m Course 2 8-2 Classifying Angles Learn to identify angles and angle pairs. 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. A Vertex B 1 Angles are measured in degrees (°). Course 2 C 8-2 Classifying 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°. Course 2 8-2 Classifying Angles Tell whether each angle is acute, right, obtuse or straight. A. obtuse angle Course 2 B. acute angle 8-2 Insert Lesson Title Here Classifying Angles Tell whether each angle is acute, right, obtuse, or straight. A. straight angle Course 2 B. acute angle 8-2 Classifying 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 8-2 Classifying Angles Omplementary upplementary Course 2 = 90˚ + 90˚ = 180˚ 8-2 Classifying Angles Reading Math A• B• 1 • C You can name this angle ABC, CBA, B, or 1. Course 2 8-2 Classifying Angles Use the diagram to tell whether the angles are complementary, supplementary, or neither. OMP and PMQ P Q O M Since 60° + 30° = 90°, PMQ and OMP are complementary. Course 2 8-2 Classifying Angles Use the diagram to tell whether the angles are complementary, supplementary, or neither. NMO and OMR Reading Math Read mNMO as “the measure of angle NMO.” O N M Since 15° + 165° = 180°, NMO and OMR are supplementary. Course 2 R 8-2 Classifying Angles Use the diagram to tell whether the angles are complementary, supplementary, or neither. PMQ and QMR P Q M R Since 30° + 75° = 105°, PMQ and QMR are neither complementary or supplementary. Course 2 8-2 Classifying Angles Angles A and B are complementary. If mA is 56°, what is the mB? Angles P and Q are supplementary. If mP is 32°, what is the mQ? Course 2 8-6 Classifying Triangles Learn to classify triangles by their side lengths and angle measures. One way to classify triangles is by the lengths of their sides. Course 2 8-6 Classifying Triangles Triangles classified by sides A scalene triangle has no congruent sides. Course 2 8-6 Classifying Triangles Triangles classified by sides An isosceles triangle has 2 congruent sides Course 2 8-6 Classifying Triangles Triangles classified by sides In an equilateral triangle, all of the sides are congruent. Course 2 8-6 Classifying Triangles Another way to classify triangles is by the measures of their angles. Triangles classified by angles In an acute triangle, all of the angles are acute. Course 2 8-6 Classifying Triangles Triangles classified by angles An obtuse triangle has one obtuse angle. Course 2 8-6 Classifying Triangles Triangles classified by angles A right triangle has one right angle. Course 2 8-6 Classifying Triangles Classify each triangle according to its sides and angles. A. isosceles Two congruent sides acute Three acute angles This is an isosceles acute triangle. B. scalene right No congruent sides One right angle This is a scalene right triangle. Course 2 8-6 Classifying Triangles Classify each triangle according to its sides and angles. C. equilateral Three congruent sides acute Three acute angles This is an equilateral acute triangle. D. scalene obtuse No congruent sides One obtuse angle (exceeds 90°) This is a scalene obtuse triangle. Course 2 8-6 Insert Lesson Title Here Classifying Triangles Classify each triangle according to its sides and angles. E. isosceles Two congruent sides obtuse One obtuse angle This is an isosceles obtuse triangle. F. isosceles right Two congruent sides One right angle This is an isosceles right triangle. Course 2 8-6 Classifying Triangles Identify the different types of triangles in the figure, and determine how many of each there are. Course 2 Type How many Name Scalene 2 ABD, BCD Isosceles 2 ACE, ABC Right ABD, BCD Obtuse 2 1 Acute 1 ACE ABC 8-6 Insert Lesson Title Here Classifying Triangles Identify the different types of triangles in the figure, and determine how many of each there are. A I B J D H G Course 2 C Type Isosceles F How many 5 E Name DJA, JDG HJI, BCD DFE Obtuse 2 DJA, ADG Acute 4 JDG, JHI, BCD, DEF 8-6 Classifying Insert Lesson Triangles Title Here Lesson Quiz Classify each triangle according to its sides and angles. 1. 7ft, 8ft, 12ft scalene 2. 45°, 90°, 45° right 3. 12, 9, 12 isosceles 4. 120°, 20°, 40° obtuse 5. Identify the different types of triangles in the figure and determine how many of each there are. 1 isosceles acute triangle, 1 equilateral triangle, 1 scalene right triangle Course 2