Congruent Triangles

1. SECTION 5-5
Congruent Triangles

2. ESSENTIAL QUESTION
How do you use postulates to identify congruent triangles?
Where you’ll see this:
Engineering, art, recreation

3. VOCABULARY
1. Congruent Triangles:
2. Side-Side-Side Postulate (SSS):
3. Side-Angle-Side Postulate (SAS):

4. VOCABULARY
1. Congruent Triangles: Triangles where corresponding sides are
the same length and corresponding angles are the same
measure
2. Side-Side-Side Postulate (SSS):
3. Side-Angle-Side Postulate (SAS):

5. VOCABULARY
1. Congruent Triangles: Triangles where corresponding sides are
the same length and corresponding angles are the same
measure
2. Side-Side-Side Postulate (SSS): When you are given three
corresponding sets of sides of the triangles as congruent,
then the triangles are congruent
3. Side-Angle-Side Postulate (SAS):

6. VOCABULARY
1. Congruent Triangles: Triangles where corresponding sides are
the same length and corresponding angles are the same
measure
2. Side-Side-Side Postulate (SSS): When you are given three
corresponding sets of sides of the triangles as congruent,
then the triangles are congruent
3. Side-Angle-Side Postulate (SAS): When you are given two
corresponding sets of sides and the included angle of the
sides as congruent, then the triangles are congruent

7. VOCABULARY
4. Angle-Side-Angle Postulate (ASA):
5. Included Angle:
6. Included Side:

8. VOCABULARY
4. Angle-Side-Angle Postulate (ASA): When you are given two
corresponding angles and the included side of the
triangles as congruent, then the triangles are congruent
5. Included Angle:
6. Included Side:

9. VOCABULARY
4. Angle-Side-Angle Postulate (ASA): When you are given two
corresponding angles and the included side of the
triangles as congruent, then the triangles are congruent
5. Included Angle: The angle formed between two given sides
6. Included Side:

10. VOCABULARY
4. Angle-Side-Angle Postulate (ASA): When you are given two
corresponding angles and the included side of the
triangles as congruent, then the triangles are congruent
5. Included Angle: The angle formed between two given sides
6. Included Side: The side formed between two given angles

11. VOCABULARY
4. Angle-Side-Angle Postulate (ASA): When you are given two
corresponding angles and the included side of the
triangles as congruent, then the triangles are congruent
5. Included Angle: The angle formed between two given sides
6. Included Side: The side formed between two given angles
These are ways to prove triangles as congruent: SSS, SAS, ASA

12. ACTIVITY
Materials: Protractor, ruler

13. ACTIVITY
Materials: Protractor, ruler
1. Draw a line segment that is 8 cm long.

14. ACTIVITY
Materials: Protractor, ruler
1. Draw a line segment that is 8 cm long.
2. From one of the endpoints, create a 50° angle.

15. ACTIVITY
Materials: Protractor, ruler
1. Draw a line segment that is 8 cm long.
2. From one of the endpoints, create a 50° angle.
3. Create a line segment at that angle that is 4 cm long.

16. ACTIVITY
Materials: Protractor, ruler
1. Draw a line segment that is 8 cm long.
2. From one of the endpoints, create a 50° angle.
3. Create a line segment at that angle that is 4 cm long.
4. Connect that new endpoint to the other original
endpoint you haven’t used.

17. ACTIVITY
Materials: Protractor, ruler
1. Draw a line segment that is 8 cm long.
2. From one of the endpoints, create a 50° angle.
3. Create a line segment at that angle that is 4 cm long.
4. Connect that new endpoint to the other original
endpoint you haven’t used.
5. Compare your triangle with some neighbors. What do
you notice?

18. ACTIVITY
Materials: Protractor, ruler

19. ACTIVITY
Materials: Protractor, ruler
1. Draw a line segment that is 3 cm long.

20. ACTIVITY
Materials: Protractor, ruler
1. Draw a line segment that is 3 cm long.
2. From one of the endpoints, create a 35° angle.

21. ACTIVITY
Materials: Protractor, ruler
1. Draw a line segment that is 3 cm long.
2. From one of the endpoints, create a 35° angle.
2. From the other endpoint, create a 75° angle so the ray points
toward the 35° angle.

22. ACTIVITY
Materials: Protractor, ruler
1. Draw a line segment that is 3 cm long.
2. From one of the endpoints, create a 35° angle.
2. From the other endpoint, create a 75° angle so the ray points
toward the 35° angle.
4. Connect the two rays if they don’t intersect.

23. ACTIVITY
Materials: Protractor, ruler
1. Draw a line segment that is 3 cm long.
2. From one of the endpoints, create a 35° angle.
2. From the other endpoint, create a 75° angle so the ray points
toward the 35° angle.
4. Connect the two rays if they don’t intersect.
5. Compare your triangle with some neighbors. What do
you notice?

24. EXAMPLE 1
State whether each pair of triangles is congruent. If so,
name the congruence and the appropriate reason why.
A D
B C E
F

25. EXAMPLE 1
State whether each pair of triangles is congruent. If so,
name the congruence and the appropriate reason why.
A D
B C E
F
Yes

26. EXAMPLE 1
State whether each pair of triangles is congruent. If so,
name the congruence and the appropriate reason why.
A D
B C E
F
Yes VABC ≅VDEF

27. EXAMPLE 1
State whether each pair of triangles is congruent. If so,
name the congruence and the appropriate reason why.
A D
B C E
F
Yes VABC ≅VDEF SSS

28. EXAMPLE 1
State whether each pair of triangles is congruent. If so,
name the congruence and the appropriate reason why.
G
H I
J
K L

29. EXAMPLE 1
State whether each pair of triangles is congruent. If so,
name the congruence and the appropriate reason why.
G
H I
J
K L
Yes

30. EXAMPLE 1
State whether each pair of triangles is congruent. If so,
name the congruence and the appropriate reason why.
G
H I
J
K L
Yes VGHI ≅VJKL

31. EXAMPLE 1
State whether each pair of triangles is congruent. If so,
name the congruence and the appropriate reason why.
G
H I
J
K L
Yes VGHI ≅VJKL SAS

32. EXAMPLE 1
State whether each pair of triangles is congruent. If so,
name the congruence and the appropriate reason why.
M
N
O
P
Q
R

33. EXAMPLE 1
State whether each pair of triangles is congruent. If so,
name the congruence and the appropriate reason why.
M
N
O
P
Q
R
Yes

34. EXAMPLE 1
State whether each pair of triangles is congruent. If so,
name the congruence and the appropriate reason why.
M
N
O
P
Q
R
Yes VMON ≅VPRQ

35. EXAMPLE 1
State whether each pair of triangles is congruent. If so,
name the congruence and the appropriate reason why.
M
N
O
P
Q
R
Yes VMON ≅VPRQ ASA

36. EXAMPLE 2
Why is it that Angle-Angle-Angle (AAA) does not give
congruent triangles?

37. EXAMPLE 2
Why is it that Angle-Angle-Angle (AAA) does not give
congruent triangles?
If all the angles are the same, the sides can be different
sizes (similar triangles), like with equilateral triangles

38. EXAMPLE 2
Why is it that Angle-Angle-Angle (AAA) does not give
congruent triangles?
If all the angles are the same, the sides can be different
sizes (similar triangles), like with equilateral triangles

39. EXAMPLE 2
Why is it that Angle-Angle-Angle (AAA) does not give
congruent triangles?
If all the angles are the same, the sides can be different
sizes (similar triangles), like with equilateral triangles

40. EXAMPLE 3
VMAN ≅VBOY, where MA = 3 in, AN = 5 in, and YB = 7 in.
m∠AMN = 37° and m∠OYB = 23°.
a. Find the lengths of the missing sides.
A O
M B
N Y

41. EXAMPLE 3
VMAN ≅VBOY, where MA = 3 in, AN = 5 in, and YB = 7 in.
m∠AMN = 37° and m∠OYB = 23°.
a. Find the lengths of the missing sides.
A O
M B
N Y
OB = 3 in

42. EXAMPLE 3
VMAN ≅VBOY, where MA = 3 in, AN = 5 in, and YB = 7 in.
m∠AMN = 37° and m∠OYB = 23°.
a. Find the lengths of the missing sides.
A O
M B
N Y
OB = 3 in OY = 5 in

43. EXAMPLE 3
VMAN ≅VBOY, where MA = 3 in, AN = 5 in, and YB = 7 in.
m∠AMN = 37° and m∠OYB = 23°.
a. Find the lengths of the missing sides.
A O
M B
N Y
OB = 3 in OY = 5 in MN = 7 in

44. EXAMPLE 3
VMAN ≅VBOY, where MA = 3 in, AN = 5 in, and YB = 7 in.
m∠AMN = 37° and m∠OYB = 23°.
a. Find the measures of the missing angles.
A O
M B
N Y

45. EXAMPLE 3
VMAN ≅VBOY, where MA = 3 in, AN = 5 in, and YB = 7 in.
m∠AMN = 37° and m∠OYB = 23°.
a. Find the measures of the missing angles.
A O
M B
N Y
m∠OBY = 37°

46. EXAMPLE 3
VMAN ≅VBOY, where MA = 3 in, AN = 5 in, and YB = 7 in.
m∠AMN = 37° and m∠OYB = 23°.
a. Find the measures of the missing angles.
A O
M B
N Y
m∠OBY = 37° m∠ANM = 23°

47. EXAMPLE 3
VMAN ≅VBOY, where MA = 3 in, AN = 5 in, and YB = 7 in.
m∠AMN = 37° and m∠OYB = 23°.
a. Find the measures of the missing angles.
A O
M B
N Y
m∠OBY = 37° m∠ANM = 23°
180 − 37 − 23 =

48. EXAMPLE 3
VMAN ≅VBOY, where MA = 3 in, AN = 5 in, and YB = 7 in.
m∠AMN = 37° and m∠OYB = 23°.
a. Find the measures of the missing angles.
A O
M B
N Y
m∠OBY = 37° m∠ANM = 23°
180 − 37 − 23 = 120

49. EXAMPLE 3
VMAN ≅VBOY, where MA = 3 in, AN = 5 in, and YB = 7 in.
m∠AMN = 37° and m∠OYB = 23°.
a. Find the measures of the missing angles.
A O
M B
N Y
m∠OBY = 37° m∠ANM = 23°
180 − 37 − 23 = 120 m∠MAN ≅ m∠BOY = 120°

50. HOMEWORK

51. HOMEWORK
p. 214 #1-25
“It is not because things are difficult that we do not dare;
it is because we do not dare that they are difficult.”
- Seneca