1. SWBAT… classify triangles in the coordinate plane
Thurs, 3/6
SWBAT… classify triangles in the coordinate plane
Agenda
Warm-up: (10 min)
Classifying triangles (40 min)
Warm-Up:
Write your HW in your planners
Homework:
Isosceles and Equilateral Triangles
#1 – #8
#9: Is the triangle scalene, isosceles, or equilateral A(0, 1), B(4, 1), C(7, 0) 1

2. Unit 5: Classifying Triangles

3. Classification means put things into a group according to how they are alike.

4. We will break this group of animals into smaller groups.

5. Can't Fly
Can Fly
The same animals can be put into different groups depending on what we look at when we classify them.
Extinct
Still Living

6. Today you will learn how triangles can be classified in two different ways...

7. Think of all the different kinds of triangles you know.
Did you come up with all of these?
Acute Obtuse Right
Scalene Isosceles Equilateral

8. Triangle The three endpoints are called vertices.
A polygon with 3 angles and 3 straight sides.
The three endpoints are called vertices.

9. Classifying by side lengths
Isosceles
at least two
Scalene
none
Equilateral
all 3

10. Scalene Triangle
All sides are different lengths.

11. Isosceles Triangle
Two out of the three sides are equal lengths.

12. Isosceles Triangle Theorem
If two sides of a triangle are congruent, then the angles opposite those sides are congruent.

13. Ex. If AC = BC, name two congruent angles.

14. Equilateral Triangle
All sides have the same length

15. Properties of Equilateral Triangles
A triangle is equilateral if and only if it is has three congruent angles (all the measures would then be 600.)

16. d = 5 Divide each side by 3. KL = 7, LM = 7, KM = 7
Ex. KLM is an equilateral triangle with KL = d + 2, LM = 12 – d, KM = 4d – 13. Find d and the measure of each side.
4d – 13 = d Substitution
3d – 13 = Subtract d from each side.
3d = Add 13 to each side.
d = Divide each side by 3.
KL = 7, LM = 7, KM = 7
Example 1-3a

17. Classify this triangle by its sides.
ISOSCELES

18. Classify this triangle by its sides.
SCALENE

19. Classify this triangle by its sides.
EQUILATERAL

20. Classify the following triangles by their sides. Use these signals:
Scalene
Isosceles
Equilateral

21. Classify by sides. Give the best name.
Scalene
Isosceles
Equilateral

22. Classify by sides. Give the best name.
Scalene
Isosceles
Equilateral

23. Classify by sides. Give the best name.
Scalene
Isosceles
Equilateral

24. What formula do you use to determine if a triangle is scalene, isosceles, or equilateral?
Answer: The terms scalene, isosceles, and equilateral have to do with side lengths of a triangle so you use the Distance Formula.

25. Classifying by angle measures
Acute
acute
right
Right
Obtuse
obtuse

26. Acute Triangle
All three angles are less than 900.
800
400
600

27. Obtuse Triangle
One of the three angles is more than 900
200
300
1300

28. Right Triangle
One of the three angles is exactly 900

29. Classify the following triangles by their sides. Use these signals:
Acute
Obtuse
Right

30. Classify by angles.
Acute
Obtuse
Right

31. Classify by angles.
1000
Acute
Obtuse
Right

32. Classify by angles.
850
450
500
Acute
Obtuse
Right

33. A B C D E
Now you should be able to classify any triangle by both its side lengths and its angles.

34. Classify the triangles by sides lengths and angles
a) b) c) 7
40°
15° 25 24
70°
70°
120°
45°
Solutions:
Scalene, Right
Isosceles, Acute
Scalene, Obtuse

35. Example 1
Classify a triangle in a coordinate plane
Determine whether PQO with vertices at P(-1, 2), Q(6, 3), O(0, 0), is scalene, isosceles, or equilateral. Explain.
SOLUTION
Use the distance formula to find the side lengths. OP = y 2 – 1 ( ) x + = 2 – ( )
(– 1 ) + 5
2.2 OQ = y 2 – 1 ( ) x + 2 = – ( ) 6 + 3 45
6.7 PQ = y 2 – 1 ( ) x + 3 – 2 ( ) 6 + =
(– 1 ) 50
7.1

36. PQO is a scalene triangle since none of the sides are congruent.
EXAMPLE
Classify a triangle in a coordinate plane (continued)
PQO is a scalene triangle since none of the sides are congruent.
Explanation

37. HW: Isosceles and Equilateral Triangles
#1 – #8
#9: Is ABC scalene, isosceles,
or equilateral A(0, 1), B(4, 1), C(7, 0)

38. Using the ruler, draw triangles with the following side measures:
a.) 3cm, 4cm, 6cm
b.) 2cm, 2cm, 6cm

39. Triangle Inequality Theorem
The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
Ex: Can these be the measures of a triangle?
a.) 3cm, 4cm, 6cm
b.) 2cm, 2cm, 6cm

40. Example: Find value of x and missing side measurement

41. Ex. Find the measure of each side of equilateral  RST with RS = 2x + 2, ST = 3x, and TR = 5x – 4.
5x – 4 = 2x + 2 x = 2 RS = 6 ST = 6 TR = 6

42. Ex. Find the measure of each side of isosceles  ABC with AB = BC if AB = 4y, BC = 3y + 2, and AC = 3y.
3y + 2 = 4y y = 2 AB = 8 BC = 8 AC = 6

43. Ex. Find x of isosceles right  WZY if angle YWZ = 900, WZ = WY, and WYZ = 3x.
3x + 3x + 90 = 180 x = 15

44. Example: Find missing angle measurements

45. c. equilateral triangles
Ex: Identify the indicated triangles in the figure.
a. isosceles triangles
Answer: ADE, ABE
b. scalene triangles
Answer: ABC, BCE, BDE, CDE, ACD, ABD
c. equilateral triangles
Answer: None!
Example 1-2c

46. Exit Slip
Is triangle A(0, 1), B(4, 4), and C(7,0) scalene, isosceles or equilateral. Explain.
Answer:
AB = 5
BC = 5
CA = 7.1
Since AB = Triangle ABC is isosceles since two of the sides are congruent.

47. #1 – #4: Find x:
4x – 4
3x + 8
600
1.) 2.) 3.) 4.) 5.) Is triangle A(0, 1), B(4, 4), and C(7,0) scalene, isosceles or equilateral. Explain.
6x0
2x0
400
(4x – 5)0

48. SWBAT… classify triangles in the coordinate plane
Mon, 3/10
SWBAT… classify triangles in the coordinate plane
Agenda
Warm-up: (10 min)
4 Examples (25 min)
Review HW (10 min)
Warm-Up: Find the missing angles:
HW: Re-do 5 problems - Worksheet
<1 = 630
<2 = 630
<3 = 380 48

49. Warm-Up: What is Congruent?
AB  ________
BD  _______  _______  _______
CBE  ________  BCE
BDE  ________
ABC  ________

50. Example: Find missing angle measurements

51. Name the missing coordinates of isosceles right triangle ABC.
Answer: C(0, 0); A(0, d)

52. Name the missing coordinates of isosceles right triangle SRQ.
Answer: Q(0, 0); S(c, c)

53. Find the missing angles.

54. Warm-Up: Find the missing angles.

55. Warm-Up Find the missing angles.

56. Warm-Up: Find the missing angles.

57. What do you know about the Pythagorean Theorem?
Homework: Collected.
What do you know about the Pythagorean Theorem?
Formula?
When and why it’s used?
Solve for x: 10 x 3 6 4 x