Download ExamView - AAS ASA and HL Quiz.tst

Name: ________________________ Class: ___________________ Date: __________
ID: A
AAS, ASA, and HL Quiz
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Using the information about John, Jason, and Julie, can you uniquely determine the distances from John to
Julie and from Julie to Jason? Explain your answer.
Statement 1: John and Jason are standing 12 feet apart.
Statement 2: The angle from Julie to John to Jason measures 31°.
Statement 3: The angle from John to Jason to Julie measures 49°.
a.
b.
c.
d.
____
No. There is no unique configuration.
Yes. They form a unique triangle by SAS.
Yes. They form a unique triangle by ASA.
Yes. They form a unique triangle by SSS.
2. Determine if you can use ASA to prove ∆CBA ≅ ∆CED. Explain.
a.
b.
c.
d.
AC ≅ DC is given. ∠CAB ≅ ∠CDE because both are right angles. No other congruence
relationships can be determined, so ASA cannot be applied.
AC ≅ DC is given. ∠CAB ≅ ∠CDE because both are right angles. By the Adjacent
Angles Theorem, ∠ACB ≅ ∠DCE . Therefore, ∆CBA ≅ ∆CED by ASA.
AC ≅ DC is given. ∠CAB ≅ ∠CDE because both are right angles. By the Vertical
Angles Theorem, ∠ACB ≅ ∠DCE . Therefore, ∆CBA ≅ ∆CED by ASA.
AC ≅ DC is given. ∠CAB ≅ ∠CDE because both are right angles. By the Vertical
Angles Theorem, ∠ACB ≅ ∠DCE . Therefore, ∆CBA ≅ ∆CED by SAS.
1
Name: ________________________
____
ID: A
3. For these triangles, select the triangle congruence statement and the postulate or theorem that supports it.
a.
b.
c.
d.
∆ABC ≅
∆ABC ≅
∆ABC ≅
∆ABC ≅
∆JLK , HL
∆JKL, HL
∆JLK , SAS
∆JKL, SAS
2
ID: A
AAS, ASA, and HL Quiz
Answer Section
MULTIPLE CHOICE
1. ANS: C
Statements 2 and 3 determine the measures of two angles of the triangle.
Statement 1 determines the length of the included side.
By ASA, the triangle must be unique.
Feedback
A
B
C
D
Draw a diagram. There is enough information to determine a unique triangle.
There is not enough information for SAS. Draw a diagram to help you.
Correct!
There is not enough information for SSS. Draw a diagram to help you.
PTS: 1
DIF: Average
REF: 1a814442-4683-11df-9c7d-001185f0d2ea
OBJ: 4-5.1 Problem-Solving Application
LOC: MTH.C.14.06.01.005
TOP: 4-5 Triangle Congruence: ASA, AAS, and HL
KEY: application | triangle congruence
DOK: DOK 2
2. ANS: C
AC ≅ DC is given. ∠CAB ≅ ∠CDE because both are right angles. By the Vertical Angles Theorem,
∠ACB ≅ ∠DCE . Therefore, ∆CBA ≅ ∆CED by ASA.
Feedback
A
B
C
D
Look for vertical angles.
Adjacent angles are angles in a plane that have their vertex and one side in common but
have no interior points in common. Angle ACB and angle DCE are not adjacent angles.
Correct!
Use ASA, not SAS, to prove the triangles congruent.
PTS:
OBJ:
LOC:
KEY:
1
DIF: Basic
4-5.2 Applying ASA Congruence
MTH.C.11.08.02.02.02.006
proof | congruent triangles | ASA
REF:
STA:
TOP:
DOK:
1
1a816b52-4683-11df-9c7d-001185f0d2ea
NY.NYLES.MTH.05.GEO.G.G.28
4-5 Triangle Congruence: ASA, AAS, and HL
DOK 2
ID: A
3. ANS: B
Because ∠BAC and ∠KJL are right angles, ∆ABC and ∆JKL are right triangles.
You are given a pair of congruent legs AC ≅ JL and a pair of congruent hypotenuses CB ≅ LK .
So a hypotenuse and a leg of ∆ABC are congruent to the corresponding hypotenuse and leg of ∆JKL.
∆ABC ≅ ∆JKL by HL.
Feedback
A
B
C
D
Segment AC is congruent to segment JL. Make sure the triangle vertices correspond
accordingly.
Correct!
Segment AC is congruent to segment JL. Make sure the triangle vertices correspond
accordingly. For SAS, the angle is included between the sides.
For SAS, the angle is included between the sides.
PTS:
STA:
LOC:
TOP:
DOK:
1
DIF: Advanced
REF: 1a86300a-4683-11df-9c7d-001185f0d2ea
NY.NYLES.MTH.05.GEO.G.G.28
MTH.C.11.08.02.02.02.010 | MTH.C.11.08.02.02.02.011
4-5 Triangle Congruence: ASA, AAS, and HL
KEY: proof | congruent triangles | HL
DOK 3
2
Name: ________________________ Class: ___________________ Date: __________
AAS, ASA, and HL Quiz
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Determine if you can use ASA to prove ∆CBA ≅ ∆CED. Explain.
a.
b.
c.
d.
AC ≅ DC is given. ∠CAB ≅ ∠CDE because both are right angles. By the Vertical
Angles Theorem, ∠ACB ≅ ∠DCE . Therefore, ∆CBA ≅ ∆CED by ASA.
AC ≅ DC is given. ∠CAB ≅ ∠CDE because both are right angles. By the Vertical
Angles Theorem, ∠ACB ≅ ∠DCE . Therefore, ∆CBA ≅ ∆CED by SAS.
AC ≅ DC is given. ∠CAB ≅ ∠CDE because both are right angles. No other congruence
relationships can be determined, so ASA cannot be applied.
AC ≅ DC is given. ∠CAB ≅ ∠CDE because both are right angles. By the Adjacent
Angles Theorem, ∠ACB ≅ ∠DCE . Therefore, ∆CBA ≅ ∆CED by ASA.
1
ID: B
Name: ________________________
____
2. For these triangles, select the triangle congruence statement and the postulate or theorem that supports it.
a.
b.
c.
d.
____
ID: B
∆ABC ≅
∆ABC ≅
∆ABC ≅
∆ABC ≅
∆JLK , SAS
∆JKL, HL
∆JLK , HL
∆JKL, SAS
3. Using the information about John, Jason, and Julie, can you uniquely determine the distances from John to
Julie and from Julie to Jason? Explain your answer.
Statement 1: John and Jason are standing 12 feet apart.
Statement 2: The angle from Julie to John to Jason measures 31°.
Statement 3: The angle from John to Jason to Julie measures 49°.
a.
b.
c.
d.
Yes. They form a unique triangle by SAS.
Yes. They form a unique triangle by SSS.
Yes. They form a unique triangle by ASA.
No. There is no unique configuration.
2
ID: B
AAS, ASA, and HL Quiz
Answer Section
MULTIPLE CHOICE
1. ANS: A
AC ≅ DC is given. ∠CAB ≅ ∠CDE because both are right angles. By the Vertical Angles Theorem,
∠ACB ≅ ∠DCE . Therefore, ∆CBA ≅ ∆CED by ASA.
Feedback
A
B
C
D
Correct!
Use ASA, not SAS, to prove the triangles congruent.
Look for vertical angles.
Adjacent angles are angles in a plane that have their vertex and one side in common but
have no interior points in common. Angle ACB and angle DCE are not adjacent angles.
PTS: 1
DIF: Basic
REF: 1a816b52-4683-11df-9c7d-001185f0d2ea
OBJ: 4-5.2 Applying ASA Congruence STA: NY.NYLES.MTH.05.GEO.G.G.28
LOC: MTH.C.11.08.02.02.02.006
TOP: 4-5 Triangle Congruence: ASA, AAS, and HL
KEY: proof | congruent triangles | ASA
DOK: DOK 2
2. ANS: B
Because ∠BAC and ∠KJL are right angles, ∆ABC and ∆JKL are right triangles.
You are given a pair of congruent legs AC ≅ JL and a pair of congruent hypotenuses CB ≅ LK .
So a hypotenuse and a leg of ∆ABC are congruent to the corresponding hypotenuse and leg of ∆JKL.
∆ABC ≅ ∆JKL by HL.
Feedback
A
B
C
D
Segment AC is congruent to segment JL. Make sure the triangle vertices correspond
accordingly. For SAS, the angle is included between the sides.
Correct!
Segment AC is congruent to segment JL. Make sure the triangle vertices correspond
accordingly.
For SAS, the angle is included between the sides.
PTS:
STA:
LOC:
TOP:
DOK:
1
DIF: Advanced
REF: 1a86300a-4683-11df-9c7d-001185f0d2ea
NY.NYLES.MTH.05.GEO.G.G.28
MTH.C.11.08.02.02.02.010 | MTH.C.11.08.02.02.02.011
4-5 Triangle Congruence: ASA, AAS, and HL
KEY: proof | congruent triangles | HL
DOK 3
1
ID: B
3. ANS: C
Statements 2 and 3 determine the measures of two angles of the triangle.
Statement 1 determines the length of the included side.
By ASA, the triangle must be unique.
Feedback
A
B
C
D
There is not enough information for SAS. Draw a diagram to help you.
There is not enough information for SSS. Draw a diagram to help you.
Correct!
Draw a diagram. There is enough information to determine a unique triangle.
PTS:
OBJ:
TOP:
DOK:
1
DIF: Average
REF: 1a814442-4683-11df-9c7d-001185f0d2ea
4-5.1 Problem-Solving Application
LOC: MTH.C.14.06.01.005
4-5 Triangle Congruence: ASA, AAS, and HL
KEY: application | triangle congruence
DOK 2
2
Name: ________________________ Class: ___________________ Date: __________
AAS, ASA, and HL Quiz
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Determine if you can use ASA to prove ∆CBA ≅ ∆CED. Explain.
a.
b.
c.
d.
AC ≅ DC is given. ∠CAB ≅ ∠CDE because both are right angles. No other congruence
relationships can be determined, so ASA cannot be applied.
AC ≅ DC is given. ∠CAB ≅ ∠CDE because both are right angles. By the Vertical
Angles Theorem, ∠ACB ≅ ∠DCE . Therefore, ∆CBA ≅ ∆CED by ASA.
AC ≅ DC is given. ∠CAB ≅ ∠CDE because both are right angles. By the Vertical
Angles Theorem, ∠ACB ≅ ∠DCE . Therefore, ∆CBA ≅ ∆CED by SAS.
AC ≅ DC is given. ∠CAB ≅ ∠CDE because both are right angles. By the Adjacent
Angles Theorem, ∠ACB ≅ ∠DCE . Therefore, ∆CBA ≅ ∆CED by ASA.
1
ID: C
Name: ________________________
____
2. For these triangles, select the triangle congruence statement and the postulate or theorem that supports it.
a.
b.
c.
d.
____
ID: C
∆ABC ≅
∆ABC ≅
∆ABC ≅
∆ABC ≅
∆JKL, SAS
∆JLK , SAS
∆JKL, HL
∆JLK , HL
3. Using the information about John, Jason, and Julie, can you uniquely determine the distances from John to
Julie and from Julie to Jason? Explain your answer.
Statement 1: John and Jason are standing 12 feet apart.
Statement 2: The angle from Julie to John to Jason measures 31°.
Statement 3: The angle from John to Jason to Julie measures 49°.
a.
b.
c.
d.
Yes. They form a unique triangle by SSS.
Yes. They form a unique triangle by SAS.
No. There is no unique configuration.
Yes. They form a unique triangle by ASA.
2
ID: C
AAS, ASA, and HL Quiz
Answer Section
MULTIPLE CHOICE
1. ANS: B
AC ≅ DC is given. ∠CAB ≅ ∠CDE because both are right angles. By the Vertical Angles Theorem,
∠ACB ≅ ∠DCE . Therefore, ∆CBA ≅ ∆CED by ASA.
Feedback
A
B
C
D
Look for vertical angles.
Correct!
Use ASA, not SAS, to prove the triangles congruent.
Adjacent angles are angles in a plane that have their vertex and one side in common but
have no interior points in common. Angle ACB and angle DCE are not adjacent angles.
PTS: 1
DIF: Basic
REF: 1a816b52-4683-11df-9c7d-001185f0d2ea
OBJ: 4-5.2 Applying ASA Congruence STA: NY.NYLES.MTH.05.GEO.G.G.28
LOC: MTH.C.11.08.02.02.02.006
TOP: 4-5 Triangle Congruence: ASA, AAS, and HL
KEY: proof | congruent triangles | ASA
DOK: DOK 2
2. ANS: C
Because ∠BAC and ∠KJL are right angles, ∆ABC and ∆JKL are right triangles.
You are given a pair of congruent legs AC ≅ JL and a pair of congruent hypotenuses CB ≅ LK .
So a hypotenuse and a leg of ∆ABC are congruent to the corresponding hypotenuse and leg of ∆JKL.
∆ABC ≅ ∆JKL by HL.
Feedback
A
B
C
D
For SAS, the angle is included between the sides.
Segment AC is congruent to segment JL. Make sure the triangle vertices correspond
accordingly. For SAS, the angle is included between the sides.
Correct!
Segment AC is congruent to segment JL. Make sure the triangle vertices correspond
accordingly.
PTS:
STA:
LOC:
TOP:
DOK:
1
DIF: Advanced
REF: 1a86300a-4683-11df-9c7d-001185f0d2ea
NY.NYLES.MTH.05.GEO.G.G.28
MTH.C.11.08.02.02.02.010 | MTH.C.11.08.02.02.02.011
4-5 Triangle Congruence: ASA, AAS, and HL
KEY: proof | congruent triangles | HL
DOK 3
1
ID: C
3. ANS: D
Statements 2 and 3 determine the measures of two angles of the triangle.
Statement 1 determines the length of the included side.
By ASA, the triangle must be unique.
Feedback
A
B
C
D
There is not enough information for SSS. Draw a diagram to help you.
There is not enough information for SAS. Draw a diagram to help you.
Draw a diagram. There is enough information to determine a unique triangle.
Correct!
PTS:
OBJ:
TOP:
DOK:
1
DIF: Average
REF: 1a814442-4683-11df-9c7d-001185f0d2ea
4-5.1 Problem-Solving Application
LOC: MTH.C.14.06.01.005
4-5 Triangle Congruence: ASA, AAS, and HL
KEY: application | triangle congruence
DOK 2
2