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 Adjacent 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 Complementary 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 , 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 Transversal Equidistant at all points
A line that intersects two or more lines at different points

15. 7.2 cont. Corresponding Angles Alternate Interior AnglesB
Corresponding Angles
Lie on same side of the transversal
Have corresponding positions
Are congruent ONLY when lines are parallel C D 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 more lines 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 , 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. ABC DEF)

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 , 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. (at least 2 congruent sides)
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. isosceles acute triangle
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. Page 320, 2-18 even
7.4 - Homework

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

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

39. 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:
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 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: Common Polygons:
Art, architecture, tile patterns
Common Polygons:
Polygon Name
Number of Sides
Triangle 3
Quadrilateral 4
Pentagon 5
Hexagon 6
Heptagon 7
Octagon 8
Nonagon 9
Decagon 10
Dodecagon 12

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. Octagon = 8 sides Example 1:
Find the sum of the measures of the interior angles of an octagon.
Octagon = 8 sides

47. 7.5 cont. Hexagon = 6 sides 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:

51. 7.5 - Homework
Page , 2-28 even, SKIP 6, 22

52. Bell Ringer (7.6) Get out yesterday’s homework assignment
Get out your notebook and prepare to take notes on Section 7.6
Find the measure of each angle of a regular polygon with 14 sides. Round to the nearest tenth.
DO NOT LOSE THE FORMULA SHEET!!

53. 7.6 – Areas of Polygons (Page 328)
Essential Question:
How do we find the area of a parallelogram, triangle, and trapezoid?

54. 7.6 cont. Application: Area: Construction Farming Architecture
Engineering
Area:
Number of square units a figure encloses

55. 7.6 cont. Area of a Triangle: 𝑨= 𝟏 𝟐 𝒃𝒉 A = Area b = base h = height
Any side of triangle can be the base
Height of triangle is perpendicular distance between base and opposite vertex

56. 7.6 cont. 𝐴= 1 2 𝑏ℎ 𝐴= 1 2 20 9.6 𝐴=96m2 Example 1:
Find the area of the following triangle:
𝐴= 1 2 𝑏ℎ 𝐴=
𝐴=96m2

57. 7.6 cont. 𝑨=𝒃𝒉 Area of a Parallelogram:
A parallelogram can be divided into two congruent triangles
Each triangle is half the area of the parallelogram

58. 7.6 cont. 𝑨=𝒃𝒉 𝑨= 𝟏𝟎 𝟓 𝑨=𝟓𝟎cm2 Example 2:
Find the area of the following parallelogram:
𝑨=𝒃𝒉
𝑨= 𝟏𝟎 𝟓
𝑨=𝟓𝟎cm2

59. 7.6 cont. Area of a Trapezoid: 𝑨= 𝟏 𝟐 𝒉 𝒃 𝟏 + 𝒃 𝟐
𝑨= 𝟏 𝟐 𝒉 𝒃 𝟏 + 𝒃 𝟐
Note: b1 and b2 name two related variables and have no effect on the value of the variable

60. 7.6 cont. Example 3: Find the area of the following trapezoid:
𝑨= 𝟏 𝟐 𝒉 𝒃 𝟏 + 𝒃 𝟐
𝑨= 𝟏 𝟐 𝟔 𝟏𝟑+𝟏𝟓
𝑨=𝟖𝟒m2

61. 7.6 - Closure
How do we find the area of a parallelogram, triangle, and trapezoid?
Parallelogram:
𝑨=𝒃𝒉
Triangle:
𝑨= 𝟏 𝟐 𝒃𝒉
Trapezoid:
𝑨= 𝟏 𝟐 𝒉 𝒃 𝟏 + 𝒃 𝟐

62. 7.6 - Homework
Page 331, 1-11, 15-17

63. Bell Ringer (7.7) 𝑨= 𝟏 𝟐 𝒉 𝒃 𝟏 + 𝒃 𝟐 𝑨= 𝟏 𝟐 𝟓 𝟔+𝟐.𝟓 𝑨=𝟐𝟏.𝟐𝟓
Get out yesterday’s homework assignment
Get out your notebook and prepare to take notes on Section 7.7
Find the area of the following trapezoid:
𝑨= 𝟏 𝟐 𝒉 𝒃 𝟏 + 𝒃 𝟐
𝑨= 𝟏 𝟐 𝟓 𝟔+𝟐.𝟓
𝑨=𝟐𝟏.𝟐𝟓

64. 7.7 – Circumference and Area of a Circle (Page 336)
Essential Questions:
How do we find the circumference and the area of a circle?
How can we use what we already know about area to find the area of irregular figures?

65. 7.7 cont.
Review:
Area
Radius
Diameter

66. 7.7 cont.
𝝅=𝟑.𝟏𝟒= 𝟐𝟐 𝟕

67. 7.7 cont.
Circumference:
𝑪=𝝅𝒅=𝟐𝝅𝒓
Area of a Circle:
𝑨=𝝅 𝒓 𝟐

68. 7.7 cont.
Example 1:
Find the circumference and area of a circle with a diameter of 9.2 inches.
Circumference:
𝑪=𝝅𝒅
𝑪=𝝅 𝟗.𝟐
𝑪≈𝟐𝟖.𝟗𝟏𝟒𝟑 in
Area:
𝑨=𝝅 𝒓 𝟐
𝑨=𝝅 𝟒.𝟔 𝟐
𝑨≈𝟔𝟔.𝟓𝟎𝟐𝟗 in2
9.2 in.

69. 7.7 cont.
Example 2:
Find the area of the following figure. Round to the nearest tenth.
Step 1: Find area of rectangle.
𝑨=𝒍𝒘= 𝟐𝟎 𝟒𝟓 =𝟗𝟎𝟎 ft2
Step 2: Find the area of the semicircle.
Entire circle: 𝑨=𝝅 𝒓 𝟐
Half of circle: 𝑨 𝑺 = 𝟏 𝟐 𝝅 𝒓 𝟐
𝑨 𝑺 = 𝟏 𝟐 𝝅 𝟏𝟓 𝟐
𝑨 𝑺 =𝟑𝟓𝟑.𝟔 ft2
Total Area: 𝟗𝟎𝟎+𝟑𝟓𝟑.𝟔=𝟏𝟐𝟓𝟑.𝟔 ft2

70. 7.7 - Closure
How do we find the circumference and the area of a circle?
Circumference
𝑪=𝝅𝒅=𝟐𝝅𝒓
Area of a Circle:
𝑨=𝝅 𝒓 𝟐
How can we use what we already know about area to find the area of irregular figures?
Split irregular figures into figures you know how to work with
Find area of each figure you know and add them all together

71. Page even, 26-30
7.7 - Homework

72. Bell Ringer Get out your 7.7 homework assignment
Think of any clarifying questions you may have about Chapter 7
Find the radius, circumference, and area of a circle with a diameter of 10.5cm.
Radius = 𝟏 𝟐 𝟏𝟎.𝟓 =𝟓.𝟐𝟓cm
Circumference = 𝟐𝝅𝒓=𝟐𝝅 𝟓.𝟐𝟓 =𝟑𝟐.𝟗𝟖𝟔𝟕
Area = 𝝅 𝒓 𝟐 =𝝅 𝟓.𝟐𝟓 𝟐 =𝟖𝟓.𝟓𝟗𝟎𝟏

73. 7.1, Review (Page 346)

74. 7.3, Review (Page 347)

75. 7.5 - Review (Page 347)

76. 7.6, Review (Page 347)

77. Flatland/Big Bang Theory Clips

78. TEST TOMORROW!! Sections 7.1-7.7 Homework: Page 348, 1-29 Study:
Notes
Problems from today’s review