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Learn to name, measure, classify, estimate, and draw angles .

7-2. Angles. Course 1. Learn to name, measure, classify, estimate, and draw angles. 7-2. Angles. Course 1. Insert Lesson Title Here. Vocabulary. angle vertex acute angle right angle obtuse angle straight angle. 7-2. Angles. Course 1.

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Learn to name, measure, classify, estimate, and draw angles .

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  1. 7-2 Angles Course 1 Learn to name, measure, classify, estimate, and draw angles.

  2. 7-2 Angles Course 1 Insert Lesson Title Here Vocabulary angle vertex acute angle right angle obtuse angle straight angle

  3. 7-2 Angles Course 1 An angle is formed by two rays with a common endpoint, called the vertex. An angle can be named by its vertex or by its vertex and a point from each ray. The middle point in the name should always be the vertex. Angles are measured in degrees. The number of degrees determines the type of angle. Use the symbol °to show degrees: 90° means “90 degrees.”

  4. 7-2 Angles Course 1 An acute anglemeasures less than 90°. A right anglemeasures exactly 90°.

  5. 7-2 Angles Course 1 An obtuse anglemeasures more than 90° and less than 180°. A straight anglemeasures exactly 180°.

  6. 7-2 Angles F H G Course 1 Additional Example 1: Measuring an Angle with a Protractor Use a protractor to measure the angle. Tell what type of angle it is. • Place the center point of the protractor on the vertex of the angle.

  7. 7-2 Angles Course 1 To estimate the measure of an angle, compare it with an angle whose measure you already know. A right angle has half the measure of a straight angle. A 45° angle has half the measure of a right angle.

  8. 7-2 Angles Course 1 Insert Lesson Title Here Lesson Quiz Use a protractor to draw an angle with the given measure. Tell what type of angle it is. 1. 140° 2. 20° 3. Draw a right angle. 4. Is the angle shown closer to 30° or 120°? obtuse acute 30°

  9. 7-3 Angle Relationships Course 1 Learn to understand relationships of angles.

  10. 7-3 Angle Relationships Course 1 Insert Lesson Title Here Vocabulary congruent vertical angles adjacent angles complementary angles supplementary angles

  11. 7-3 Angle Relationships M N 160° 20° 20° R 160° Q P MRP and NRQ are vertical angles. MRN and PRQ are vertical angles Course 1 When angles have the same measure, they are said to be congruent. Vertical angles are formed opposite each other when two lines intersect. Vertical angles have the same measure, so they are always congruent.

  12. 7-3 Angle Relationships M N 160° 20° 20° R 160° Q P MRN and NRQ are adjacent angles. They share vertex R and RN. NRQ and QRP are adjacent angles. They share vertex R and RQ. Course 1 Adjacent angles are side by side and have a common vertex and ray. Adjacent angles may or may not be congruent.

  13. 7-3 Angle Relationships 5 and 6 are opposite each other and are formed by two intersecting lines. Course 1 Additional Example 1A: Identifying Types of Angle Pairs Identify the type of each angle pair shown. A. 5 6 They are vertical angles.

  14. 7-3 Angle Relationships 7 and 8 are side by side and have a common vertex and ray. Course 1 Additional Example 1B: Identifying Types of Angle Pairs Identify the type of each angle pair shown. B. 7 8 They are adjacent angles.

  15. 7-3 Angle Relationships 65° + 25° = 90° LMN and NMP are complementary. L N 65° 25° M P Course 1 Complementary angles are two angles whose measures have a sum of 90°.

  16. 7-3 Angle Relationships 65° + 115° = 180° GHK and KHJ are supplementary. K 65° 115° G J H Course 1 Supplementary anglesare two angles whose measures have a sum of 180°.

  17. 7-3 Angle Relationships Course 1 Additional Example 2A: Identifying an Unknown Angle Measure Find each unknown angle measure. A. The angles are complementary. The sum of the measures is 90°. 71° + a = 90° a –71°–71° a = 19° 71°

  18. 7-3 Angle Relationships Course 1 Additional Example 2B: Identifying an Unknown Angle Measure Find each unknown angle measure. B. The angles are supplementary. 125° + b = 180° The sum of the measures is 180°. –125°–125° b = 55° 125° b

  19. 7-3 Angle Relationships Course 1 Additional Example 2C: Identifying an Unknown Angle Measure Find each unknown angle measure. C. The angles are vertical angles. c 82° c = 82° Vertical angles are congruent.

  20. 7-3 Angle Relationships Course 1 Insert Lesson Title Here Lesson Quiz Give the complement of each angle. 1. 70° 2. 42° Give the supplement of each angle. 3. 120° 4. 17° 5. Identify the type of angle pair shown. 20° 48° 60° 163° adjacent

  21. 7-4 Classifying Lines Course 1 Learn to classify the different types of lines.

  22. 7-4 Classifying Lines Course 1 Insert Lesson Title Here Vocabulary parallel lines perpendicular lines skew lines intersecting lines transversal

  23. 7-3 Parallel and Perpendicular Lines Reading Math The symbol means “is parallel to.” The symbol means “is perpendicular to.” Course 2

  24. 7-4 Classifying Lines W Y Line YZ intersects line WX. YZ intersects WX. X Z B Line AB is parallel to line ML. ABML. A L M Course 1 Intersecting lines are lines that cross at one common point. Parallel linesare lines in the same plane that never intersect.

  25. 7-4 Classifying Lines R Line RS is perpendicular to line TU. RSTU. T U S Course 1 Perpendicular linesintersect to form 90° angles, or right angles. Writing Math The square inside a right angle shows that the rays of the angle are perpendicular.

  26. 7-4 Classifying Lines Line AB and line ML are skew. AB and ML are skew. A M B L Course 1 Skew lines are lines that lie in different planes. They are neither parallel nor intersecting.

  27. 7-4 Classifying Lines Course 1 Additional Example 1A: Classifying Pairs of Lines Classify each pair of lines. A. The lines intersect to form right angles. They are perpendicular.

  28. 7-4 Classifying Lines Course 1 Additional Example 1B: Classifying Pairs of Lines Classify each pair of lines. B. The lines are in different planes and are not parallel or intersecting. They are skew.

  29. 7-4 Classifying Lines Course 1 Additional Example 1C: Classifying Pairs of Lines Classify each pair of lines. C. The lines are in the same plane. They do not appear to intersect. They are parallel.

  30. 7-4 Classifying Lines Course 1 Additional Example 1D: Classifying Pairs of Lines Classify each pair of lines. D. The lines cross at one common point. They are intersecting.

  31. 7-4 Classifying Lines Course 1 Additional Example 2: Application The handrails on an escalator are in the same plane. What type of line relationship do they represent? The handrails are in the same plane and do not intersect. The lines are parallel.

  32. 7-4 Classifying Lines Course 1 Try This: Example 2 The roads are in the same plane. What type of line relationship do they represent? The lines cross at one common point. The lines are intersecting.

  33. 7-3 Parallel and Perpendicular Lines Course 2 A transversalis a line that intersects two or more lines. Eight angles are formed when a transversal intersects two lines. There are 4 interior angles and 4 exterior angles. When those two lines are parallel, all of the acute angles formed are congruent, and all of the obtuse angles formed are congruent. These obtuse and acute angles are supplementary. 1 2 3 4 5 6 7 8

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