Name: ________________________ Class: ___________________ Date: __________
4.3 Congruent Triangles Quiz
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Given: ∆ABC ≅ ∆MNO
Identify all pairs of congruent corresponding parts.
a.
b.
c.
d.
____
∠A ≅
∠A ≅
∠A ≅
∠A ≅
∠M , ∠B ≅ ∠N , ∠C ≅ ∠O,
∠M , ∠B ≅ ∠O, ∠C ≅ ∠N ,
∠M , ∠B ≅ ∠N , ∠C ≅ ∠O,
∠O, ∠B ≅ ∠N , ∠C ≅ ∠M ,
AB ≅
AB ≅
AB ≅
AB ≅
MN , BC ≅ NO, AC ≅
MN , BC ≅ NO, AC ≅
MO, BC ≅ NO, AC ≅
NO, BC ≅ MN , AC ≅
2. Given that ∆ABC ≅ ∆DEC and m∠E = 23°, find m∠ACB.
a.
b.
c.
d.
m∠ACB = 77°
m∠ACB = 67°
m∠ACB = 23°
m∠ACB = 113°
1
MO
MO
MN
MO
ID: A
Name: ________________________
ID: A
BONUS
____
3. Given: RT ⊥SU , ∠SRT ≅ ∠URT , RS ≅ RU . T is the midpoint of SU .
Prove: ∆RTS ≅ ∆RTU
Complete the proof.
Proof:
Statements
1. RT ⊥SU
2. ∠RTS and ∠RTU are right angles.
3. ∠RTS ≅ ∠RTU
4. ∠SRT ≅ ∠URT
5. ∠S ≅ ∠U
6. RS ≅ RU
7. T is the midpoint of SU .
8. ST ≅ UT
9. RT ≅ RT
10. ∆RTS ≅ ∆RTU
a.
[1] Definition of right angles
[2] Third Angles Theorem
[3] Transitive Property of Congruence
b.
[1] Definition of perpendicular lines
[2] Third Angles Theorem
[3] Reflexive Property of Congruence
c.
[1] Definition of perpendicular lines
[2] Vertical Angles Theorem
[3] Symmetric Property of Congruence
d.
[1] Definition of perpendicular lines
[2] Third Angles Theorem
[3] Symmetric Property of Congruence
Reasons
1. Given
2. [1]
3. Right Angle Congruence Theorem
4. Given
5. [2]
6. Given
7. Given
8. Definition of midpoint
9. [3]
10. Definition of congruent triangles
2
ID: A
4.3 Congruent Triangles Quiz
Answer Section
MULTIPLE CHOICE
1. ANS: A
Corresponding angles and corresponding sides are parts which lie in the same position in the triangles.
Corresponding angles: ∠A ≅ ∠M , ∠B ≅ ∠N , ∠C ≅ ∠O
Corresponding sides: AB ≅ MN , BC ≅ NO, AC ≅ MO
Feedback
A
B
C
D
Correct!
The corresponding angles should be in the same position in triangle ABC and triangle
MNO.
The corresponding sides should be in the same position in triangle ABC and triangle
MNO.
Check that the corresponding angles and sides are congruent.
PTS:
OBJ:
STA:
LOC:
KEY:
1
DIF: Basic
REF: 1a7093be-4683-11df-9c7d-001185f0d2ea
4-3.1 Naming Congruent Corresponding Parts
NAT: NT.CCSS.MTH.10.9-12.G.SRT.5
NY.NYLES.MTH.05.GEO.G.RP.2
MTH.C.11.01.02.03.002 | MTH.C.11.02.02.002
TOP: 4-3 Congruent Triangles
correspondence | corresponding parts
DOK: DOK 1
1
ID: A
2. ANS: B
m∠DCE + m∠CED + m∠EDC = 180°
m∠DCE + 23° + 90° = 180°
m∠DCE + 113° = 180°
m∠DCE = 67°
∠DCE ≅ ∠BCA
m∠DCE = m∠BCA
m∠ACB = 67°
Triangle Sum Theorem
Substitution.
Simplify.
Subtract 113 from both sides.
Corresponding parts of congruent triangles are
congruent.
Definition of congruent angles
Corresponding parts of congruent triangles are
congruent.
Feedback
A
B
C
D
The sum of all angle measures in a triangle is equal to 180 degrees.
Correct!
Check which angles are corresponding angles.
Check your calculations.
PTS:
OBJ:
STA:
LOC:
KEY:
DOK:
1
DIF: Average
REF: 1a72f61a-4683-11df-9c7d-001185f0d2ea
4-3.2 Using Corresponding Parts of Congruent Triangles NAT: NT.CCSS.MTH.10.9-12.G.SRT.5
NY.NYLES.MTH.05.GEO.G.G.30 | NY.NYLES.MTH.05.GEO.G.G.36
MTH.C.11.02.02.001 | MTH.C.11.03.02.04.002
TOP: 4-3 Congruent Triangles
triangle sum theorem | congruent triangles | corresponding parts
DOK 2
2
ID: A
3. ANS: B
Proof:
Statements
1. RT ⊥SU
2. ∠RTS and ∠RTU are right angles.
3. ∠RTS ≅ ∠RTU
4. ∠SRT ≅ ∠URT
5. ∠S ≅ ∠U
6. RS ≅ RU
7. T is the midpoint of SU .
8. ST ≅ UT
9. RT ≅ RT
10. ∆RTS ≅ ∆RTU
Reasons
1. Given
2. Definition of perpendicular lines
3. Right Angle Congruence Theorem
4. Given
5. Third Angles Theorem
6. Given
7. Given
8. Definition of midpoint
9. Reflexive Property of Congruence
10. Definition of congruent triangles
Feedback
A
B
C
D
Use the definition of perpendicular lines to show that the lines intersect to form right
angles.
Correct!
Angle S and angle U are not vertical angles. Use a different justification for Reason 5.
Use the correct property to show that the part is congruent to itself.
PTS:
OBJ:
STA:
LOC:
KEY:
1
DIF: Average
REF: 1a731d2a-4683-11df-9c7d-001185f0d2ea
4-3.3 Proving Triangles Congruent NAT: NT.CCSS.MTH.10.9-12.G.SRT.5
NY.NYLES.MTH.05.GEO.G.PS.4 | NY.NYLES.MTH.05.GEO.G.RP.2
MTH.P.08.02.03.017 | MTH.C.11.08.02.02.002
TOP: 4-3 Congruent Triangles
proof | congruent triangles
DOK: DOK 1
3
Name: ________________________ Class: ___________________ Date: __________
4.3 Congruent Triangles Quiz
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Given: ∆ABC ≅ ∆MNO
Identify all pairs of congruent corresponding parts.
a.
b.
c.
d.
____
∠A ≅
∠A ≅
∠A ≅
∠A ≅
∠M , ∠B ≅ ∠O, ∠C ≅ ∠N ,
∠M , ∠B ≅ ∠N , ∠C ≅ ∠O,
∠M , ∠B ≅ ∠N , ∠C ≅ ∠O,
∠O, ∠B ≅ ∠N , ∠C ≅ ∠M ,
AB ≅
AB ≅
AB ≅
AB ≅
MN , BC ≅ NO, AC ≅
MN , BC ≅ NO, AC ≅
MO, BC ≅ NO, AC ≅
NO, BC ≅ MN , AC ≅
2. Given that ∆ABC ≅ ∆DEC and m∠E = 23°, find m∠ACB.
a.
b.
c.
d.
m∠ACB = 67°
m∠ACB = 77°
m∠ACB = 23°
m∠ACB = 113°
1
MO
MO
MN
MO
ID: B
Name: ________________________
ID: B
BONUS
____
3. Given: RT ⊥SU , ∠SRT ≅ ∠URT , RS ≅ RU . T is the midpoint of SU .
Prove: ∆RTS ≅ ∆RTU
Complete the proof.
Proof:
Statements
1. RT ⊥SU
2. ∠RTS and ∠RTU are right angles.
3. ∠RTS ≅ ∠RTU
4. ∠SRT ≅ ∠URT
5. ∠S ≅ ∠U
6. RS ≅ RU
7. T is the midpoint of SU .
8. ST ≅ UT
9. RT ≅ RT
10. ∆RTS ≅ ∆RTU
a.
[1] Definition of right angles
[2] Third Angles Theorem
[3] Transitive Property of Congruence
b.
[1] Definition of perpendicular lines
[2] Third Angles Theorem
[3] Reflexive Property of Congruence
c.
[1] Definition of perpendicular lines
[2] Third Angles Theorem
[3] Symmetric Property of Congruence
[1] Definition of perpendicular lines
[2] Vertical Angles Theorem
[3] Symmetric Property of Congruence
d.
Reasons
1. Given
2. [1]
3. Right Angle Congruence Theorem
4. Given
5. [2]
6. Given
7. Given
8. Definition of midpoint
9. [3]
10. Definition of congruent triangles
2
ID: B
4.3 Congruent Triangles Quiz
Answer Section
MULTIPLE CHOICE
1. ANS: B
Corresponding angles and corresponding sides are parts which lie in the same position in the triangles.
Corresponding angles: ∠A ≅ ∠M , ∠B ≅ ∠N , ∠C ≅ ∠O
Corresponding sides: AB ≅ MN , BC ≅ NO, AC ≅ MO
Feedback
A
B
C
D
The corresponding angles should be in the same position in triangle ABC and triangle
MNO.
Correct!
The corresponding sides should be in the same position in triangle ABC and triangle
MNO.
Check that the corresponding angles and sides are congruent.
PTS:
OBJ:
STA:
LOC:
KEY:
1
DIF: Basic
REF: 1a7093be-4683-11df-9c7d-001185f0d2ea
4-3.1 Naming Congruent Corresponding Parts
NAT: NT.CCSS.MTH.10.9-12.G.SRT.5
NY.NYLES.MTH.05.GEO.G.RP.2
MTH.C.11.01.02.03.002 | MTH.C.11.02.02.002
TOP: 4-3 Congruent Triangles
correspondence | corresponding parts
DOK: DOK 1
1
ID: B
2. ANS: A
m∠DCE + m∠CED + m∠EDC = 180°
m∠DCE + 23° + 90° = 180°
m∠DCE + 113° = 180°
m∠DCE = 67°
∠DCE ≅ ∠BCA
m∠DCE = m∠BCA
m∠ACB = 67°
Triangle Sum Theorem
Substitution.
Simplify.
Subtract 113 from both sides.
Corresponding parts of congruent triangles are
congruent.
Definition of congruent angles
Corresponding parts of congruent triangles are
congruent.
Feedback
A
B
C
D
Correct!
The sum of all angle measures in a triangle is equal to 180 degrees.
Check which angles are corresponding angles.
Check your calculations.
PTS:
OBJ:
STA:
LOC:
KEY:
DOK:
1
DIF: Average
REF: 1a72f61a-4683-11df-9c7d-001185f0d2ea
4-3.2 Using Corresponding Parts of Congruent Triangles NAT: NT.CCSS.MTH.10.9-12.G.SRT.5
NY.NYLES.MTH.05.GEO.G.G.30 | NY.NYLES.MTH.05.GEO.G.G.36
MTH.C.11.02.02.001 | MTH.C.11.03.02.04.002
TOP: 4-3 Congruent Triangles
triangle sum theorem | congruent triangles | corresponding parts
DOK 2
2
ID: B
3. ANS: B
Proof:
Statements
1. RT ⊥SU
2. ∠RTS and ∠RTU are right angles.
3. ∠RTS ≅ ∠RTU
4. ∠SRT ≅ ∠URT
5. ∠S ≅ ∠U
6. RS ≅ RU
7. T is the midpoint of SU .
8. ST ≅ UT
9. RT ≅ RT
10. ∆RTS ≅ ∆RTU
Reasons
1. Given
2. Definition of perpendicular lines
3. Right Angle Congruence Theorem
4. Given
5. Third Angles Theorem
6. Given
7. Given
8. Definition of midpoint
9. Reflexive Property of Congruence
10. Definition of congruent triangles
Feedback
A
B
C
D
Use the definition of perpendicular lines to show that the lines intersect to form right
angles.
Correct!
Use the correct property to show that the part is congruent to itself.
Angle S and angle U are not vertical angles. Use a different justification for Reason 5.
PTS:
OBJ:
STA:
LOC:
KEY:
1
DIF: Average
REF: 1a731d2a-4683-11df-9c7d-001185f0d2ea
4-3.3 Proving Triangles Congruent NAT: NT.CCSS.MTH.10.9-12.G.SRT.5
NY.NYLES.MTH.05.GEO.G.PS.4 | NY.NYLES.MTH.05.GEO.G.RP.2
MTH.P.08.02.03.017 | MTH.C.11.08.02.02.002
TOP: 4-3 Congruent Triangles
proof | congruent triangles
DOK: DOK 1
3
Name: ________________________ Class: ___________________ Date: __________
4.3 Congruent Triangles Quiz
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Given: ∆ABC ≅ ∆MNO
Identify all pairs of congruent corresponding parts.
a.
b.
c.
d.
____
∠A ≅
∠A ≅
∠A ≅
∠A ≅
∠M , ∠B ≅ ∠N , ∠C ≅ ∠O,
∠M , ∠B ≅ ∠N , ∠C ≅ ∠O,
∠O, ∠B ≅ ∠N , ∠C ≅ ∠M ,
∠M , ∠B ≅ ∠O, ∠C ≅ ∠N ,
AB ≅
AB ≅
AB ≅
AB ≅
MN , BC ≅ NO, AC ≅
MO, BC ≅ NO, AC ≅
NO, BC ≅ MN , AC ≅
MN , BC ≅ NO, AC ≅
2. Given that ∆ABC ≅ ∆DEC and m∠E = 23°, find m∠ACB.
a.
b.
c.
d.
m∠ACB = 23°
m∠ACB = 67°
m∠ACB = 77°
m∠ACB = 113°
1
MO
MN
MO
MO
ID: C
Name: ________________________
ID: C
BONUS
____
3. Given: RT ⊥SU , ∠SRT ≅ ∠URT , RS ≅ RU . T is the midpoint of SU .
Prove: ∆RTS ≅ ∆RTU
Complete the proof.
Proof:
Statements
1. RT ⊥SU
2. ∠RTS and ∠RTU are right angles.
3. ∠RTS ≅ ∠RTU
4. ∠SRT ≅ ∠URT
5. ∠S ≅ ∠U
6. RS ≅ RU
7. T is the midpoint of SU .
8. ST ≅ UT
9. RT ≅ RT
10. ∆RTS ≅ ∆RTU
a.
b.
Reasons
1. Given
2. [1]
3. Right Angle Congruence Theorem
4. Given
5. [2]
6. Given
7. Given
8. Definition of midpoint
9. [3]
10. Definition of congruent triangles
[1] Definition of perpendicular lines
[2] Third Angles Theorem
[3] Symmetric Property of Congruence
[1] Definition of perpendicular lines
[2] Third Angles Theorem
[3] Reflexive Property of Congruence
c.
[1] Definition of perpendicular lines
[2] Vertical Angles Theorem
[3] Symmetric Property of Congruence
d.
[1] Definition of right angles
[2] Third Angles Theorem
[3] Transitive Property of Congruence
2
ID: C
4.3 Congruent Triangles Quiz
Answer Section
MULTIPLE CHOICE
1. ANS: A
Corresponding angles and corresponding sides are parts which lie in the same position in the triangles.
Corresponding angles: ∠A ≅ ∠M , ∠B ≅ ∠N , ∠C ≅ ∠O
Corresponding sides: AB ≅ MN , BC ≅ NO, AC ≅ MO
Feedback
A
B
C
D
Correct!
The corresponding sides should be in the same position in triangle ABC and triangle
MNO.
Check that the corresponding angles and sides are congruent.
The corresponding angles should be in the same position in triangle ABC and triangle
MNO.
PTS:
OBJ:
STA:
LOC:
KEY:
1
DIF: Basic
REF: 1a7093be-4683-11df-9c7d-001185f0d2ea
4-3.1 Naming Congruent Corresponding Parts
NAT: NT.CCSS.MTH.10.9-12.G.SRT.5
NY.NYLES.MTH.05.GEO.G.RP.2
MTH.C.11.01.02.03.002 | MTH.C.11.02.02.002
TOP: 4-3 Congruent Triangles
correspondence | corresponding parts
DOK: DOK 1
1
ID: C
2. ANS: B
m∠DCE + m∠CED + m∠EDC = 180°
m∠DCE + 23° + 90° = 180°
m∠DCE + 113° = 180°
m∠DCE = 67°
∠DCE ≅ ∠BCA
m∠DCE = m∠BCA
m∠ACB = 67°
Triangle Sum Theorem
Substitution.
Simplify.
Subtract 113 from both sides.
Corresponding parts of congruent triangles are
congruent.
Definition of congruent angles
Corresponding parts of congruent triangles are
congruent.
Feedback
A
B
C
D
Check which angles are corresponding angles.
Correct!
The sum of all angle measures in a triangle is equal to 180 degrees.
Check your calculations.
PTS:
OBJ:
STA:
LOC:
KEY:
DOK:
1
DIF: Average
REF: 1a72f61a-4683-11df-9c7d-001185f0d2ea
4-3.2 Using Corresponding Parts of Congruent Triangles NAT: NT.CCSS.MTH.10.9-12.G.SRT.5
NY.NYLES.MTH.05.GEO.G.G.30 | NY.NYLES.MTH.05.GEO.G.G.36
MTH.C.11.02.02.001 | MTH.C.11.03.02.04.002
TOP: 4-3 Congruent Triangles
triangle sum theorem | congruent triangles | corresponding parts
DOK 2
2
ID: C
3. ANS: B
Proof:
Statements
1. RT ⊥SU
2. ∠RTS and ∠RTU are right angles.
3. ∠RTS ≅ ∠RTU
4. ∠SRT ≅ ∠URT
5. ∠S ≅ ∠U
6. RS ≅ RU
7. T is the midpoint of SU .
8. ST ≅ UT
9. RT ≅ RT
10. ∆RTS ≅ ∆RTU
Reasons
1. Given
2. Definition of perpendicular lines
3. Right Angle Congruence Theorem
4. Given
5. Third Angles Theorem
6. Given
7. Given
8. Definition of midpoint
9. Reflexive Property of Congruence
10. Definition of congruent triangles
Feedback
A
B
C
D
Use the correct property to show that the part is congruent to itself.
Correct!
Angle S and angle U are not vertical angles. Use a different justification for Reason 5.
Use the definition of perpendicular lines to show that the lines intersect to form right
angles.
PTS:
OBJ:
STA:
LOC:
KEY:
1
DIF: Average
REF: 1a731d2a-4683-11df-9c7d-001185f0d2ea
4-3.3 Proving Triangles Congruent NAT: NT.CCSS.MTH.10.9-12.G.SRT.5
NY.NYLES.MTH.05.GEO.G.PS.4 | NY.NYLES.MTH.05.GEO.G.RP.2
MTH.P.08.02.03.017 | MTH.C.11.08.02.02.002
TOP: 4-3 Congruent Triangles
proof | congruent triangles
DOK: DOK 1
3