SECTION 5-5Congruent Triangles
Mon, Jan 31
ESSENTIAL QUESTION
How do you use postulates to identify congruent triangles?
Where you’ll see this:
Engineering, art, recreation
Mon, Jan 31
VOCABULARY1. Congruent Triangles:
2. Side-Side-Side Postulate (SSS):
3. Side-Angle-Side Postulate (SAS):
Mon, Jan 31
VOCABULARY1. 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
VOCABULARY1. 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
VOCABULARY1. 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
VOCABULARY4. Angle-Side-Angle Postulate (ASA):
5. Included Angle:
6. Included Side:
Mon, Jan 31
VOCABULARY4. 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
VOCABULARY4. 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
VOCABULARY4. 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
VOCABULARY4. 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
ACTIVITY
Materials: Protractor, ruler
Mon, Jan 31
ACTIVITY
Materials: Protractor, ruler
1. Draw a line segment that is 8 cm long.
Mon, Jan 31
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
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
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
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
ACTIVITY
Materials: Protractor, ruler
Mon, Jan 31
ACTIVITY
Materials: Protractor, ruler
1. Draw a line segment that is 3 cm long.
Mon, Jan 31
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
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
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
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
EXAMPLE 1State whether each pair of triangles is congruent. If so, name the congruence and the appropriate reason why.
A
B CFE
D
Mon, Jan 31
EXAMPLE 1State whether each pair of triangles is congruent. If so, name the congruence and the appropriate reason why.
A
B CFE
D
Yes
Mon, Jan 31
EXAMPLE 1State whether each pair of triangles is congruent. If so, name the congruence and the appropriate reason why.
A
B CFE
D
Yes ABC ≅DEF
Mon, Jan 31
EXAMPLE 1State whether each pair of triangles is congruent. If so, name the congruence and the appropriate reason why.
A
B CFE
D
Yes ABC ≅DEF SSS
Mon, Jan 31
EXAMPLE 1State whether each pair of triangles is congruent. If so, name the congruence and the appropriate reason why.
G
H I
LK
J
Mon, Jan 31
EXAMPLE 1State whether each pair of triangles is congruent. If so, name the congruence and the appropriate reason why.
Yes
G
H I
LK
J
Mon, Jan 31
EXAMPLE 1State whether each pair of triangles is congruent. If so, name the congruence and the appropriate reason why.
Yes GHI ≅ JKL
G
H I
LK
J
Mon, Jan 31
EXAMPLE 1State whether each pair of triangles is congruent. If so, name the congruence and the appropriate reason why.
Yes GHI ≅ JKL SAS
G
H I
LK
J
Mon, Jan 31
EXAMPLE 1State whether each pair of triangles is congruent. If so, name the congruence and the appropriate reason why.
Q
P
R
O
M
N
Mon, Jan 31
EXAMPLE 1State whether each pair of triangles is congruent. If so, name the congruence and the appropriate reason why.
Yes
Q
P
R
O
M
N
Mon, Jan 31
EXAMPLE 1State whether each pair of triangles is congruent. If so, name the congruence and the appropriate reason why.
Yes MON ≅PRQ
Q
P
R
O
M
N
Mon, Jan 31
EXAMPLE 1State whether each pair of triangles is congruent. If so, name the congruence and the appropriate reason why.
Yes MON ≅PRQ ASA
Q
P
R
O
M
N
Mon, Jan 31
EXAMPLE 2Why is it that Angle-Angle-Angle (AAA) does not give
congruent triangles?
Mon, Jan 31
EXAMPLE 2Why 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
EXAMPLE 2Why 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
EXAMPLE 2Why 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
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.
M
A
N
B
O
Y
Mon, Jan 31
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.
M
A
N
B
O
Y
OB = 3 in
Mon, Jan 31
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.
M
A
N
B
O
Y
OB = 3 in OY = 5 in
Mon, Jan 31
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.
M
A
N
B
O
Y
OB = 3 in OY = 5 in MN = 7 in
Mon, Jan 31
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.
M
A
N
B
O
Y
Mon, Jan 31
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.
M
A
N
B
O
Y
m∠OBY = 37°
Mon, Jan 31
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.
M
A
N
B
O
Y
m∠OBY = 37° m∠ANM = 23°
Mon, Jan 31
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.
M
A
N
B
O
Y
m∠OBY = 37° m∠ANM = 23°
180− 37 − 23 =Mon, Jan 31
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.
M
A
N
B
O
Y
m∠OBY = 37° m∠ANM = 23°
180− 37 − 23 = 120Mon, Jan 31
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.
M
A
N
B
O
Y
m∠OBY = 37° m∠ANM = 23°
180− 37 − 23 = 120 m∠MAN ≅ m∠BOY = 120°
Mon, Jan 31
PROBLEM SET
Mon, Jan 31
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.”
- SenecaMon, Jan 31
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