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):
Mon, Jan 31
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):
Mon, Jan 31
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
Mon, Jan 31
7. VOCABULARY
4. Angle-Side-Angle Postulate (ASA):
5. Included Angle:
6. Included Side:
Mon, Jan 31
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:
Mon, Jan 31
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:
Mon, Jan 31
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
Mon, Jan 31
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
Mon, Jan 31
12. ACTIVITY
Materials: Protractor, ruler
Mon, Jan 31
13. ACTIVITY
Materials: Protractor, ruler
1. Draw a line segment that is 8 cm long.
Mon, Jan 31
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.
Mon, Jan 31
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.
Mon, Jan 31
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.
Mon, Jan 31
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 classmates in class
tomorrow. What do you notice?
Mon, Jan 31
18. ACTIVITY
Materials: Protractor, ruler
Mon, Jan 31
19. ACTIVITY
Materials: Protractor, ruler
1. Draw a line segment that is 3 cm long.
Mon, Jan 31
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.
Mon, Jan 31
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.
3. From the other endpoint, create a 75° angle so the ray points
toward the 35° angle.
Mon, Jan 31
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.
3. 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.
Mon, Jan 31
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.
3. 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 classmates in class
tomorrow. What do you notice?
Mon, Jan 31
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
Mon, Jan 31
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
Mon, Jan 31
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 ABC ≅DEF
Mon, Jan 31
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 ABC ≅DEF SSS
Mon, Jan 31
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
Mon, Jan 31
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
Mon, Jan 31
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 GHI ≅ JKL
Mon, Jan 31
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 GHI ≅ JKL SAS
Mon, Jan 31
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
Mon, Jan 31
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
Mon, Jan 31
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 MON ≅PRQ
Mon, Jan 31
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 MON ≅PRQ ASA
Mon, Jan 31
36. EXAMPLE 2
Why is it that Angle-Angle-Angle (AAA) does not give
congruent triangles?
Mon, Jan 31
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
Mon, Jan 31
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
Mon, Jan 31
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
Mon, Jan 31
40. EXAMPLE 3
MAN ≅BOY, 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
Mon, Jan 31
41. EXAMPLE 3
MAN ≅BOY, 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
Mon, Jan 31
42. EXAMPLE 3
MAN ≅BOY, 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
Mon, Jan 31
43. EXAMPLE 3
MAN ≅BOY, 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
Mon, Jan 31
44. EXAMPLE 3
MAN ≅BOY, where MA = 3 in, AN = 5 in, and YB = 7 in.
m∠AMN = 37° and m∠OYB = 23°.
b. Find the measures of the missing angles.
A O
M B
N Y
Mon, Jan 31
45. EXAMPLE 3
MAN ≅BOY, where MA = 3 in, AN = 5 in, and YB = 7 in.
m∠AMN = 37° and m∠OYB = 23°.
b. Find the measures of the missing angles.
A O
M B
N Y
m∠OBY = 37°
Mon, Jan 31
46. EXAMPLE 3
MAN ≅BOY, where MA = 3 in, AN = 5 in, and YB = 7 in.
m∠AMN = 37° and m∠OYB = 23°.
b. Find the measures of the missing angles.
A O
M B
N Y
m∠OBY = 37° m∠ANM = 23°
Mon, Jan 31
47. EXAMPLE 3
MAN ≅BOY, where MA = 3 in, AN = 5 in, and YB = 7 in.
m∠AMN = 37° and m∠OYB = 23°.
b. Find the measures of the missing angles.
A O
M B
N Y
m∠OBY = 37° m∠ANM = 23°
180 − 37 − 23 =
Mon, Jan 31
48. EXAMPLE 3
MAN ≅BOY, where MA = 3 in, AN = 5 in, and YB = 7 in.
m∠AMN = 37° and m∠OYB = 23°.
b. Find the measures of the missing angles.
A O
M B
N Y
m∠OBY = 37° m∠ANM = 23°
180 − 37 − 23 = 120
Mon, Jan 31
49. EXAMPLE 3
MAN ≅BOY, where MA = 3 in, AN = 5 in, and YB = 7 in.
m∠AMN = 37° and m∠OYB = 23°.
b. 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°
Mon, Jan 31
51. PROBLEM SET
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
Mon, Jan 31
