Int Math 2 Section 5-5 1011
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Transcript of Int Math 2 Section 5-5 1011
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SECTION 5-5Congruent Triangles
Mon, Jan 31
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ESSENTIAL QUESTION
How do you use postulates to identify congruent triangles?
Where you’ll see this:
Engineering, art, recreation
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VOCABULARY1. Congruent Triangles:
2. Side-Side-Side Postulate (SSS):
3. Side-Angle-Side Postulate (SAS):
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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):
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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
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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
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VOCABULARY4. Angle-Side-Angle Postulate (ASA):
5. Included Angle:
6. Included Side:
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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:
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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:
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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
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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
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ACTIVITY
Materials: Protractor, ruler
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ACTIVITY
Materials: Protractor, ruler
1. Draw a line segment that is 8 cm long.
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ACTIVITY
Materials: Protractor, ruler
1. Draw a line segment that is 8 cm long.
2. From one of the endpoints, create a 50° angle.
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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
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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
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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
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ACTIVITY
Materials: Protractor, ruler
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ACTIVITY
Materials: Protractor, ruler
1. Draw a line segment that is 3 cm long.
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ACTIVITY
Materials: Protractor, ruler
1. Draw a line segment that is 3 cm long.
2. From one of the endpoints, create a 35° angle.
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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
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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
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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
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EXAMPLE 1State whether each pair of triangles is congruent. If so, name the congruence and the appropriate reason why.
A
B CFE
D
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EXAMPLE 1State whether each pair of triangles is congruent. If so, name the congruence and the appropriate reason why.
A
B CFE
D
Yes
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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
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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
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EXAMPLE 1State whether each pair of triangles is congruent. If so, name the congruence and the appropriate reason why.
G
H I
LK
J
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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
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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
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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
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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
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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
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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
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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
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EXAMPLE 2Why is it that Angle-Angle-Angle (AAA) does not give
congruent triangles?
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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
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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
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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
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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
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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
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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
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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
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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
![Page 45: Int Math 2 Section 5-5 1011](https://reader034.fdocuments.us/reader034/viewer/2022042715/55a1e4f51a28ab94508b46f2/html5/thumbnails/45.jpg)
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
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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
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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
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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
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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
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PROBLEM SET
Mon, Jan 31
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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