1. Problem of the Day (Monday)
Alternate Interior Angles?
3 & 6, 4 & 5
1 & 4, 2 & 3, 5 & 8, 7 & 6
1 & 5, 2 & 6, 3 & 7, 4 & 8
1 & 8, 2 & 7

2. Angles Review Corresponding Angles? 1 & 2, 2 & 4, 3 & 4, 1 & 3
6 & 5, 6 & 8, 7 & 8, 5 & 7
1 & 4, 2 & 3, 5 & 8, 7 & 6
1 & 5, 2 & 6, 3 & 7, 4 & 8
1 & 8, 2 & 7 1 2 3 4 5 6 7 8

3. Supplementary Angles?
1 & 2, 2 & 4, 3 & 4, 1 & 3
6 & 5, 6 & 8, 7 & 8, 5 & 7
1 & 4, 2 & 3, 5 & 8, 7 & 6
1 & 5, 2 & 6, 3 & 7, 4 & 8
1 & 8, 2 & 7

4. Alternate Exterior Angles?
1 & 2, 2 & 4, 3 & 4, 1 & 3
6 & 5, 6 & 8, 7 & 8, 5 & 7
1 & 4, 2 & 3, 5 & 8, 7 & 6
1 & 5, 2 & 6, 3 & 7, 4 & 8
1 & 8, 2 & 7

5. Vertical Angles?
1 & 2, 2 & 4, 3 & 4, 1 & 3
6 & 5, 6 & 8, 7 & 8, 5 & 7
1 & 4, 2 & 3, 5 & 8, 7 & 6
1 & 5, 2 & 6, 3 & 7, 4 & 8
1 & 8, 2 & 7

6. Polygon:
Closed figure
Regular Polygon:
All sides are equal

7. Triangles Everywhere

16. Problem of the Day (Tuesday)
What is the measure of angle x?
720°
120°
360°
60° x

17. A regular pentagon: What is the sum of the interior angles?
What is the measure of each interior angle?
What is the sum of the exterior angles?
What is the measure of each exterior angle?

18. An irregular pentagon What is the measure of the missing angle? 90˚
130˚ ?
90˚
130˚

19. A regular hexagon:
What is the sum of the interior angles?

21. What is the measure of the missing angle?
90˚
120˚
170˚
100˚
130˚ ?

22. A regular octagon: What is the sum of the interior angles?
What is the measure of each interior angle?
What is the sum of the exterior angles?
What is the measure of each exterior angle?

23. A regular decagon: What is the sum of the interior angles?
What is the measure of each interior angle?
What is the sum of the exterior angles?
What is the measure of each exterior angle?

24. Missing Angles Challenge
Name__________________
*You may only assume that the pentagon and hexagon are regular.
a = _____
b = _____
c = _____
d = _____
e = _____
f = _____
g = _____
h = _____
i = _____
j = _____
k = _____
l = _____
m = _____
n = _____
o = _____
p = _____
q = _____
r = _____
s = _____
t = _____
u = _____
v = _____
w = _____
x = _____ l m h j g b k c n q t s i a o p r u v d x
110° e
45° f

25. Learning Target
I can… Find the exterior angles of any polygon

26. Exterior Angles of a Polygon

30. Level Five – Find the missing angles1. 3. b a 2. 4.
34˚ a b

32. Missing Angles The lines m and n are parallel
What is the measure angle b?
What is the measure of angle a?
What is the measure of angle g?
What is the measure of angle f? a
98° d f b c e g

33. Create your own puzzle Rules: You must use at least 2 regular polygons
Angle measures must be close (they do not have to be perfectly drawn to scale)
You must use a ruler
You must include 3 of the following:
complementary angles, supplementary angles, interior angles, exterior angles, corresponding angles, vertical angles

34. Problem of the Day (Tuesday)
What is the measure of angle x?
720°
120°
360°
60° x

35. A regular pentagon: What is the sum of the interior angles?
What is the measure of each interior angle?
What is the sum of the exterior angles?
What is the measure of each exterior angle?

36. Congruent Triangles
All sides are congruent and all angles are congruent H L K J I G

37. Congruent Triangles

38. SSS B E A C F D

39. SAS H L K J I G

40. ASA

41. AAS

42. Congruent Polygons Show that each pair of triangles is congruent.
QP EY Side a.
Q E Angle
Q Y Angle b.
SQ VT Side
Q T Angle
QR TU Side
QPR EYT by ASA.
SQR VTU by SAS.

45. Does AAA guarantee that two triangles are congruent? Why or why not?
Same angles, different sizes
Example:
80°
80°
50°
50°
50°
50°

49. Congruent Polygons
A surveyor drew the diagram below to find the distance from J to I across the canyon. Show that GHI KJI. Then find JK.
J H Both are right angles.
JI HI Both measure 48 ft.
KIJ GIH They are vertical angles.
So ∆GHI ∆ JI by ASA
Corresponding parts of congruent triangles are congruent.
JK corresponds to HG, so JK is 36 ft.

50. Congruent Polygons Use ABC and XYZ to answer the questions.
1.Suppose AC= XZ, AB = XY, and BC = YZ.
Write a congruence statement for the figures.
2.Suppose ABC and XYZ are congruent. If AB = 5 cm,
BC = 8 cm, and AC = 10 cm, find XZ.
3. Suppose B Y, A X, and AB XY. Why is
ABC XYZ?
∆ABC  ∆XYZ
10 cm
ASA

51. Congruent Polygons 4. Let AB = XY = 9 inches; BC = YZ = 24 inches; and
m B = 85°, m Z = 35°, and m Y = 85°. Prove that
the triangles are congruent and find m C.
∆ABC  ∆XYZ by SAS; m C =35°

52. Problem of the Day (Wednesday)
Are the two triangles congruent? Why?
Yes, because of SAS
Yes, because of ASA
Yes, because of SSS
No, because two side are congruent, no angles

53. ABC is congruent to DCB because of SAS
ABC is congruent to BCD because of AAS
The triangles are not congruent because they only have a side and angle that are congruent

54. Are the two triangles congruent? Why or why not?
Yes, because of SAS
Yes, because of ASA
Yes, because of SSA
No, because SSA is not a congruent triangle rule

55. Review Are the two triangles congruent? Why? Yes, because of SAS
Yes, because of ASA
Yes, because of SSS
No, because two side are congruent, no angles

56. Are the two triangles congruent? Why?
Yes, because of SAS
Yes, because of ASA
Yes, because of SSS
No, because two side are congruent, no angles

57. Are the two triangles congruent? Why?
Yes, because of AAS
Yes, because of ASA
Yes, because of SSS
No, because two sides are congruent, no angles

58. Is ? Why?
Yes, because of SAS
Yes, because of ASA
Yes, because of SSS
No, because two side are congruent, no angles

59. Corresponding parts
If two polygons are congruent, then their corresponding parts are congruent.
For example:
Since QRS = HGJ
That means

60. Similar Triangles Triangles are similar if:
1. All angles are congruent
2. Corresponding sides are proportional
Symbol: ABC ~ DEF
Example: E B
80°
80° 2 2 6 6
50°
50° A C 5
50°
50° D F 15

61. Corresponding Sides Sides that match ABC ~ XBY
AC corresponds to ____
AB corresponds to _____
BY corresponds to _____ X Y A C

62. Are the triangles similar?
No, ¾ is not proportional to ½ B 4 3 A 1 C D F 2

63. Are the triangles similar? Why or why not?2
1.5

64. If ABC ~ DEF, find x E B 9
40.5 A 11 C F D x

67. Other Polygons Can Be Similar Too
Other Polygons Can Be Similar Too *They still must have congruent angles and sides must be proportional B F C G 2 5 H E A D 16
If the two figures are similar, what is the measure of side EH?

68. You try!

69. Which polygons are always similar?
(hint: they always have congruent angles and they will always have proportional sides)
Rhombuses
Squares
Triangles
Pentagons

70. CPS Learning Series Questions!

71. Problem of the Day (Thursday)
If the two figures are similar, what is the value of x? 52 8 x
71.5 11
5.81
464.75 14

72. Right Triangles
hypotenuse
leg
leg

73. Pythagorean Theorem
Use when you know 2 sides of a right triangle and you need to figure out the 3rd
a² + b² = c²
a and b are lengths of sides and c is the length of the hypotenuse

74. Example a²+ b² = c² a = 3, b = 4 3² + 4² = c² 9 + 16 = c² 25 = c²

75. You try
Find the measure of
the hypotenuse x x 5 12

76. You try again!

77. You also can find the length of a side
Find the missing length
a² + b² = c²
8² + x² = 10²
64 + x² = 100
-64
x² = 36
x = 6 10 8 x

78. You try!

80. Pam is making a new sail for her sailboat pictured below
Pam is making a new sail for her sailboat pictured below. What is the height of the sail?
a² + b² = c²
a² + 10² = 26²
a² = 676
-100
a² = 576
a = 24

81. The Pythagorean Theorem
A ladder, placed 4 ft from a wall, touches the wall 11.3 ft above the ground. What is the approximate length of the ladder?
Draw a diagram to illustrate the problem.
c2 = a2 + b2
Use the Pythagorean Theorem.
c2 =
Substitute.
c2 =
c2 =
Square 4 and 11.3.
Add.
Use a calculator.
Take the square root of each side.
c =
c2 =
The length of the ladder is about 12 ft.

82. a² + b² = c²
6² + 8² = 9² ?
= 81?
100 = 81?
No, she cannot use these boards

83. Problem of the Day (Friday)

85. You Try!

86. Draw a picture!