1. corresponding Consecutive int. 5x + 7 = 9x – 63 17.5 = x
2. Use your knowledge of angle relationships to solve for x in the diagrams below. Justify your solutions by naming the geometric relationship.
corresponding
Consecutive int.
5x + 7 = 9x – 63
17.5 = x
32x + 20 = 180
x = 5

2. No, Need arrows to show parallel lines

3. How Can I Use It? Pg. 16 Angles In a Triangle
2.4
How Can I Use It?
Pg. 16
Angles In a Triangle

4. 2.4 – How Can I Use It?_____________ Angles In a Triangle
So far in this chapter, you have investigated the angle relationships created when two lines intersect, forming vertical angles. You have also investigated the relationships created when a transversal intersects two parallel lines. Today you will study the angle relationships that result when three non-parallel lines intersect, forming a triangle.

5. 2.23 – ANGLE RELATIONSHIPS
Marcos decided to study the angle relationships in triangles by making a tiling. Find the pattern below.

6. a. Color in one of the angles with a pen or pencil
a. Color in one of the angles with a pen or pencil. Then use the same color to shade every angle on the pattern that is equal to the shaded angle.

7. b. Repeat this process for the other two angles of the triangle, using a different color for each angle in the triangle. When you are done, every angle in your tiling should be shaded with one of the three colors.

8. c. Now examine your colored tiling
c. Now examine your colored tiling. What relationship can you find between the three different-colored angles? You may want to focus on the angles that form a straight angle. What does this tell you about the angles in a triangle?

9. "If a polygon is a triangle, then the sum
of the interior angles is ___________"
180°

10. d. Let us see if this works for any triangle
d. Let us see if this works for any triangle. Each team member will cut out a different type of triangle: isosceles, scalene, right, or obtuse. Rip off the angles of the triangle and put them together to form a straight line. Do these three angles all add to 180°?

12. e. How can you convince yourself that your conjecture is true for all triangles? Match the reasons to the proof below to show that the sum of the interior angles of any triangle adds to 180°.

13. Alternate interior = Alternate interior = Make Straight line
Statements
Reasons 1. 2. 3. 4.
Alternate interior =
Alternate interior =
Make Straight line
substitution

14. 2.23 – TRIANGLE ANGLE RELATIONSHIPS
Use your proof about the angles in a triangle to find x in each diagram below.

15. x = 180
2x + x = 180
x = 180
3x = 180
x = 60°
3x = 72
x = 24°

16. All sides are congruent
Type of ∆
Definition
Picture
Equilateral Triangle
All sides are congruent
CLASSIFICATION BY SIDES

17. leg leg 2 sides congruent base Type of ∆ Definition Picture
Isosceles Triangle
leg
leg
2 sides congruent
CLASSIFICATION BY SIDES
base

18. No sides are congruent Type of ∆ Definition Picture Scalene Triangle
CLASSIFICATION BY SIDES

19. All angles are congruent
Type of ∆
Definition
Picture
Equiangular
Triangle
All angles are congruent
CLASSIFICATION BY ANGLES

20. All angles are acute Type of ∆ Definition Picture Acute Triangle
CLASSIFICATION BY ANGLES

21. hypotenuse leg One right angle leg Type of ∆ Definition Picture
Right Triangle
hypotenuse
leg
One right angle
CLASSIFICATION BY ANGLES
leg

22. One obtuse angle and 2 acute angles
Type of ∆
Definition
Picture
Obtuse Triangle
One obtuse angle and 2 acute angles
CLASSIFICATION BY ANGLES

23. Classify the triangle by the best definition based on sides and angles.
scalene
right

24. equilateral
equiangular

25. isosceles
obtuse

26. 2.25 – TRIANGLE SUM THEOREM
What can the Triangle Angle Sum Theorem help you learn about special triangles?

27. a. Find the measure of each angle in an equilateral triangle
a. Find the measure of each angle in an equilateral triangle. Justify your conclusion.
180° 3
60°
60°
60°

28. b. Consider the isosceles right triangle at right
b. Consider the isosceles right triangle at right. Find the measures of all the angles.
180 – 90 2
45°
45°

29. c. What if you only know one angle of an isosceles triangle
c. What if you only know one angle of an isosceles triangle? For example, if
what are the measures of the other two angles?
180 – 34 2
34°
73°
73°

30. d. Use the fact that when the triangle is isosceles, the base angles are congruent to solve for x and y.

31. 2(22)+11 55 55
3x – 11 =
2x + 11
2y = 180
x – 11 = 11
2y = 70
x = 22
y = 35

32. 9x – 8 = 28
9x = 36
x = 4

33. 2.26 – TEAM REASONING CHALLENGE
How much can you figure out about the figure using your knowledge of angle relationships? Work with your team to find the measures of all the labeled angles in the diagram.

34. 123°
99°
81°
57°
81°
99°
123°
42°
57°
57°
123°

35. 180° 2.27 – ANGLE AND LINE RELATIONSHIPS
Use your knowledge of angle relationships to answer the questions below.
a. In the diagram at right, what is the sum of the angles x and y?
180°

36. b. While looking at the diagram below, Rianna exclaimed, "I think something is wrong with this diagram." What do you think she is referring to? Be prepared to share your ideas.

37. E

38. 0°

39. Yes,
112° + 68° = 180°

40. supplementary parallel
d. Write a conjecture based on your conclusion to this problem.
"If the measures of same-side interior angles are __________________, then the lines are _____________."
supplementary
parallel

41. e. State the angle relationship shown
e. State the angle relationship shown. Then find the value of x that makes the lines parallel.

42. Alternate interior
4x – 10 = 3x + 13
x – 10 = 13
x = 23

43. corresponding
8x – 14 = 7x + 2
x – 14 = 2
x = 16

44. Consecutive interior
20x – 2 + 6x = 180
26x – 2 = 180
26x = 182
x = 7

45. Alternate exterior
6x + 17 = 143
6x = 126
x = 21

46. 10 words Definition Mark in real life picture notation
Vocabulary Project
10 words
Definition
Mark in real life picture
notation

47. Perpendicular Line
Lines that cross at right angles A C D B

48. Coplanar Points
Points on the same plane C A B

49. Vertical Angles
Angles opposite each other that are congruent A B C D E

50. Triangle
Polygon with 3 sides A B C