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Bell Ringer

Bell Ringer. Get out your notebook and prepare to take notes on Chapter 7 List five shapes you see in the classroom. Chapter 7. 7.1 - Pairs of Angles (Page 303). Essential Questions: How do we identify types of angles?

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Bell Ringer

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  1. Bell Ringer • Get out your notebook and prepare to take notes on Chapter 7 • List five shapes you see in the classroom

  2. Chapter 7

  3. 7.1 - Pairs of Angles (Page 303) • Essential Questions: • How do we identify types of angles? • How can identifying types of angles allow us to find relationships among angles?

  4. 7.1 cont. • Vertical angles • Formed by two intersecting lines • Angles opposite one another are CONGRUENT • Congruent - have the same measure • Adjacent angles • Common vertex and common side

  5. 7.1 cont. • Example 1: • Name a pair of adjacent angles and a pair of vertical angles in the figure below: 145° • What is the measure of angle HGK?

  6. 7.1 cont. • Supplementary angles • Angles that add to 180 degrees • Complementary angles • Angles that add to 90 degrees

  7. 7.1 cont. • Example 2: • Find the measure of the supplement of the angle IGJ in the following figure: 35° • What does the supplement you found represent in the figure?

  8. 7.1 cont. • Perpendicular lines • Two lines that intersect to form a right angle

  9. 7.1 cont. • Example 3: • In the following figure, if the measure of angle DKH is 73°, find the measures of the angles GKJ and JKF: 17° 73° 73°

  10. 7.1 - Closure • How do we identify types of angles? • Vertical angles, adjacent angles • How can identifying types of angles allow us to find relationships among angles? • Complementary/supplementary angles • Identify perpendicular lines

  11. 7.1 - Homework Page 305-306, 2-32 even

  12. Bell Ringer (7.2) • Get out yesterday’s homework assignment • Get out your notebook and prepare to take notes on Section 7.2 • List two sets of parallel lines you see in the classroom

  13. 7.2 – Angles and Parallel Lines (Page 307) • Essential Questions: • What is a transversal? • What congruent angles are formed when a transversal intersects two parallel lines?

  14. 7.2 cont. • Parallel Lines • Equidistant at all points • Transversal • A line that intersects two or more linesat different points

  15. 7.2 cont. A B C D • Corresponding Angles • Lie on same side of the transversal • Have corresponding positions • Are congruent ONLY when lines are parallel E F G H • Alternate Interior Angles • Lie within a pair of lines • On opposite sides of the transversal • Are congruent ONLY when lines are parallel E F G H

  16. 7.2 cont. • Example 1: • Identify each pair of corresponding angles and each pair of alternate interior angles in the following figure:

  17. 7.2 cont. • Example 2: • If p is parallel to q in the following figure, and the measure of angle 3 is 56°, find the measure of angle 6. = 56°

  18. 7.2 cont. • Example 3: • In the figure below, explain how you know ? Alternate interior angles are congruent, therefore, lines a and b are parallel.

  19. 7.2 - Closure • What is a transversal? • A line that intersects two or morelines at different points • What congruent angles are formed when a transversal intersects two parallel lines? • Corresponding angles • Alternate interior angles

  20. 7.2 - Homework Page 309-310, 2-28 even

  21. Bell Ringer (7.3) • Get out yesterday’s homework assignment • Get out your notebook and prepare to take notes on Section 7.3 • List five polygons you see in the classroom

  22. 7.3 – Congruent Polygons (Page 312) • Essential Questions: • Which parts of congruent figures can be congruent to each other? • What are three ways we can demonstrate that two triangles are congruent?

  23. 7.3 cont. • Congruent Polygons: • Polygons that have the same size and shape • Can be slid, flipped, or turned so that one fits exactly on top of the other • Tick marks and arcs tell you which sides and angles are congruent • NOTE: When naming congruent polygons, list corresponding vertices in the same order!! (i.e. ABCDEF)

  24. 7.3 cont. • Example 1: • In the diagram below, list the congruent parts of the two figures. Then write a congruence statement.

  25. 7.3 cont. • Showing Triangles are Congruent: • Use corresponding parts • Use the following postulates: • NOTE: Order of angles and sides is important!!

  26. 7.3 cont. • Example 2: • Show that the following pair of triangles are congruent: Angle Side Angle by

  27. 7.3 - Closure • Which parts of congruent figures can be congruent to each other? • Corresponding angles and sides • What are three ways we can demonstrate that two triangles are congruent? • SSS, SAS, ASA

  28. 7.3 - Homework Page 314-316, 2-28 even SKIP 22

  29. Bell Ringer (7.4) • Get out yesterday’s homework assignment • Get out your notebook and prepare to take notes on Section 7.4 • Answer the following question: • What two characteristics do congruent polygons have in common?

  30. 7.4 – Classifying Triangles and Quadrilaterals (Page 318) • Essential Question: • How do we classify triangles and quadrilaterals?

  31. 7.4 cont. • Classifying Triangles: • Use angles and sides • 6 types: Acute (3 acute angles) Obtuse (1 obtuse angle) Right (1 right angle) Equilateral (3 congruent sides) Isosceles (at least 2 congruent sides) Scalene (no congruent sides)

  32. 7.4 cont. • Example 1: • Classify LMN by its sides and angles: 2 congruent sides 3 acute angles isosceles acute triangle

  33. 7.4 cont. • Classifying Quadrilaterals: • Use angles and sides • Name quadrilaterals by listing vertices in consecutive order

  34. 7.4 cont. • Example 2: • How would you classify the following figure? Opposite sides are parallel Adjacent sides are not equal Parallelogram

  35. 7.4 - Closure • How do we classify triangles and quadrilaterals? • Triangles – angles or congruent sides • Quadrilaterals – sides and angles

  36. 7.4 - Homework Page 320, 2-18 even

  37. Bell Ringer • Get out yesterday’s homework assignment • Think of any clarifying questions you may have about 7.1-7.4 • Draw and label a trapezoid that contains a right angle.

  38. Mimio Software • Match the angle pair with the proper name

  39. 7.1-7.3 Review (Page 317)

  40. 7.4 Review • Classify the following triangle according to its angles and sides: • A triangle’s sides are all congruent and its angles all measure 60˚. Classify the triangle. • Determine the best name for the following quadrilateral: • What is the best name for a figure that has four sides congruent, corresponding angles parallel, and all four angles congruent?

  41. QUIZ TOMORROW!! • Sections 7.1-7.4 • Homework: Page 346-347, 1-12, SKIP #5 • Study: • 7.1-7.4 Homework • Notes • Problems from today’s review

  42. Bell Ringer (7.5) • Get out your notebook and prepare to take notes on Section 7.5 • Prepare to ask questions about the 7-1-7.4 quiz

  43. 7.5 – Angles and Polygons (Page 324) • Essential Question: • How do we find the interior angle measures of a polygon?

  44. 7.5 cont. • Application: • Art, architecture, tile patterns • Common Polygons:

  45. 7.5 cont. • **Sum of the measures of the interior angles depends on the number of sides in the polygon** • Polygon Angle Sum: • For a polygon with n sides, the sum of the measures of the interior angles is as follows: °

  46. 7.5 cont. • Example 1: • Find the sum of the measures of the interior angles of an octagon. ° Octagon = 8 sides ° ° °

  47. 7.5 cont. • Example 2: • Find the missing angle measure in the following hexagon: ° ° ° ° = sum of angle measures ° Hexagon = 6 sides

  48. 7.5 cont. • Regular Polygons: • All sides and angles congruent • Equation for angle sum: °

  49. 7.5 cont. • Example 3: • A design tile is in the shape of a regular nonagon. Find the measure of each angle. ° ° = 140°

  50. 7.5 - Closure • How do we find the interior angle measures of a polygon? • For a polygon of n sides: • For a regular polygon of n sides: ° °

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