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