Mathematics
Geometry
Perpendicular bisector angle with segment:
A. None
B. Centroid
C. 90°
D. Orthocenter
Correct Answer: C
Correct theorem/construction fact: 90°.
Mathematics
Geometry
Perpendicular bisector passes through:
A. None
B. Midpoint
C. Centroid
D. Orthocenter
Correct Answer: B
Correct theorem/construction fact: Midpoint.
Mathematics
Geometry
Locus at fixed distance r from fixed point:
A. Centroid
B. None
C. Circle
D. Orthocenter
Correct Answer: C
Correct theorem/construction fact: Circle.
Mathematics
Geometry
Locus equidistant from two intersecting lines:
A. Orthocenter
B. Centroid
C. None
D. Angle bisectors
Correct Answer: D
Correct theorem/construction fact: Angle bisectors.
Mathematics
Geometry
Locus equidistant from two fixed points:
A. Perpendicular bisector
B. None
C. Orthocenter
D. Centroid
Correct Answer: A
Correct theorem/construction fact: Perpendicular bisector.
Mathematics
Geometry
With ℓ ∥ m, ∠1=78°. Find alternate interior ∠2.<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><line x1="25" y1="48" x2="235" y2="48" stroke="#1f2937" stroke-width="2"/><line x1="25" y1="132" x2="235" y2="132" stroke="#1f2937" stroke-width="2"/><line x1="75" y1="15" x2="170" y2="165" stroke="#2563eb" stroke-width="2.5"/><text x="95" y="42" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">∠1</text><text x="144" y="125" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">∠2</text><text x="25" y="23" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">ℓ ∥ m</text></svg>
A. 70°
B. 86°
C. 78°
D. 94°
Correct Answer: C
Alternate interior angles are equal: ∠2=78°.
Mathematics
Geometry
With ℓ ∥ m, ∠1=76°. Find alternate interior ∠2.<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><line x1="25" y1="48" x2="235" y2="48" stroke="#1f2937" stroke-width="2"/><line x1="25" y1="132" x2="235" y2="132" stroke="#1f2937" stroke-width="2"/><line x1="75" y1="15" x2="170" y2="165" stroke="#2563eb" stroke-width="2.5"/><text x="95" y="42" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">∠1</text><text x="144" y="125" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">∠2</text><text x="25" y="23" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">ℓ ∥ m</text></svg>
A. 92°
B. 68°
C. 84°
D. 76°
Correct Answer: D
Alternate interior angles are equal: ∠2=76°.
Mathematics
Geometry
With ℓ ∥ m, ∠1=74°. Find alternate interior ∠2.<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><line x1="25" y1="48" x2="235" y2="48" stroke="#1f2937" stroke-width="2"/><line x1="25" y1="132" x2="235" y2="132" stroke="#1f2937" stroke-width="2"/><line x1="75" y1="15" x2="170" y2="165" stroke="#2563eb" stroke-width="2.5"/><text x="95" y="42" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">∠1</text><text x="144" y="125" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">∠2</text><text x="25" y="23" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">ℓ ∥ m</text></svg>
A. 90°
B. 82°
C. 74°
D. 66°
Correct Answer: C
Alternate interior angles are equal: ∠2=74°.
Mathematics
Geometry
With ℓ ∥ m, ∠1=72°. Find alternate interior ∠2.<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><line x1="25" y1="48" x2="235" y2="48" stroke="#1f2937" stroke-width="2"/><line x1="25" y1="132" x2="235" y2="132" stroke="#1f2937" stroke-width="2"/><line x1="75" y1="15" x2="170" y2="165" stroke="#2563eb" stroke-width="2.5"/><text x="95" y="42" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">∠1</text><text x="144" y="125" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">∠2</text><text x="25" y="23" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">ℓ ∥ m</text></svg>
A. 72°
B. 88°
C. 80°
D. 64°
Correct Answer: A
Alternate interior angles are equal: ∠2=72°.
Mathematics
Geometry
With ℓ ∥ m, ∠1=70°. Find alternate interior ∠2.<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><line x1="25" y1="48" x2="235" y2="48" stroke="#1f2937" stroke-width="2"/><line x1="25" y1="132" x2="235" y2="132" stroke="#1f2937" stroke-width="2"/><line x1="75" y1="15" x2="170" y2="165" stroke="#2563eb" stroke-width="2.5"/><text x="95" y="42" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">∠1</text><text x="144" y="125" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">∠2</text><text x="25" y="23" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">ℓ ∥ m</text></svg>
A. 78°
B. 70°
C. 62°
D. 86°
Correct Answer: B
Alternate interior angles are equal: ∠2=70°.
Mathematics
Geometry
With ℓ ∥ m, ∠1=68°. Find alternate interior ∠2.<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><line x1="25" y1="48" x2="235" y2="48" stroke="#1f2937" stroke-width="2"/><line x1="25" y1="132" x2="235" y2="132" stroke="#1f2937" stroke-width="2"/><line x1="75" y1="15" x2="170" y2="165" stroke="#2563eb" stroke-width="2.5"/><text x="95" y="42" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">∠1</text><text x="144" y="125" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">∠2</text><text x="25" y="23" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">ℓ ∥ m</text></svg>
A. 84°
B. 60°
C. 76°
D. 68°
Correct Answer: D
Alternate interior angles are equal: ∠2=68°.
Mathematics
Geometry
With ℓ ∥ m, ∠1=66°. Find alternate interior ∠2.<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><line x1="25" y1="48" x2="235" y2="48" stroke="#1f2937" stroke-width="2"/><line x1="25" y1="132" x2="235" y2="132" stroke="#1f2937" stroke-width="2"/><line x1="75" y1="15" x2="170" y2="165" stroke="#2563eb" stroke-width="2.5"/><text x="95" y="42" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">∠1</text><text x="144" y="125" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">∠2</text><text x="25" y="23" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">ℓ ∥ m</text></svg>
A. 74°
B. 82°
C. 66°
D. 58°
Correct Answer: C
Alternate interior angles are equal: ∠2=66°.
Mathematics
Geometry
With ℓ ∥ m, ∠1=64°. Find alternate interior ∠2.<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><line x1="25" y1="48" x2="235" y2="48" stroke="#1f2937" stroke-width="2"/><line x1="25" y1="132" x2="235" y2="132" stroke="#1f2937" stroke-width="2"/><line x1="75" y1="15" x2="170" y2="165" stroke="#2563eb" stroke-width="2.5"/><text x="95" y="42" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">∠1</text><text x="144" y="125" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">∠2</text><text x="25" y="23" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">ℓ ∥ m</text></svg>
A. 56°
B. 72°
C. 80°
D. 64°
Correct Answer: D
Alternate interior angles are equal: ∠2=64°.
Mathematics
Geometry
With ℓ ∥ m, ∠1=62°. Find alternate interior ∠2.<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><line x1="25" y1="48" x2="235" y2="48" stroke="#1f2937" stroke-width="2"/><line x1="25" y1="132" x2="235" y2="132" stroke="#1f2937" stroke-width="2"/><line x1="75" y1="15" x2="170" y2="165" stroke="#2563eb" stroke-width="2.5"/><text x="95" y="42" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">∠1</text><text x="144" y="125" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">∠2</text><text x="25" y="23" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">ℓ ∥ m</text></svg>
A. 78°
B. 62°
C. 70°
D. 54°
Correct Answer: B
Alternate interior angles are equal: ∠2=62°.
Mathematics
Geometry
With ℓ ∥ m, ∠1=60°. Find alternate interior ∠2.<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><line x1="25" y1="48" x2="235" y2="48" stroke="#1f2937" stroke-width="2"/><line x1="25" y1="132" x2="235" y2="132" stroke="#1f2937" stroke-width="2"/><line x1="75" y1="15" x2="170" y2="165" stroke="#2563eb" stroke-width="2.5"/><text x="95" y="42" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">∠1</text><text x="144" y="125" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">∠2</text><text x="25" y="23" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">ℓ ∥ m</text></svg>
A. 52°
B. 76°
C. 68°
D. 60°
Correct Answer: D
Alternate interior angles are equal: ∠2=60°.
Mathematics
Geometry
With ℓ ∥ m, ∠1=58°. Find alternate interior ∠2.<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><line x1="25" y1="48" x2="235" y2="48" stroke="#1f2937" stroke-width="2"/><line x1="25" y1="132" x2="235" y2="132" stroke="#1f2937" stroke-width="2"/><line x1="75" y1="15" x2="170" y2="165" stroke="#2563eb" stroke-width="2.5"/><text x="95" y="42" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">∠1</text><text x="144" y="125" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">∠2</text><text x="25" y="23" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">ℓ ∥ m</text></svg>
A. 66°
B. 50°
C. 58°
D. 74°
Correct Answer: C
Alternate interior angles are equal: ∠2=58°.
Mathematics
Geometry
With ℓ ∥ m, ∠1=56°. Find alternate interior ∠2.<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><line x1="25" y1="48" x2="235" y2="48" stroke="#1f2937" stroke-width="2"/><line x1="25" y1="132" x2="235" y2="132" stroke="#1f2937" stroke-width="2"/><line x1="75" y1="15" x2="170" y2="165" stroke="#2563eb" stroke-width="2.5"/><text x="95" y="42" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">∠1</text><text x="144" y="125" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">∠2</text><text x="25" y="23" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">ℓ ∥ m</text></svg>
A. 72°
B. 48°
C. 56°
D. 64°
Correct Answer: C
Alternate interior angles are equal: ∠2=56°.
Mathematics
Geometry
With ℓ ∥ m, ∠1=54°. Find alternate interior ∠2.<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><line x1="25" y1="48" x2="235" y2="48" stroke="#1f2937" stroke-width="2"/><line x1="25" y1="132" x2="235" y2="132" stroke="#1f2937" stroke-width="2"/><line x1="75" y1="15" x2="170" y2="165" stroke="#2563eb" stroke-width="2.5"/><text x="95" y="42" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">∠1</text><text x="144" y="125" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">∠2</text><text x="25" y="23" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">ℓ ∥ m</text></svg>
A. 46°
B. 70°
C. 54°
D. 62°
Correct Answer: C
Alternate interior angles are equal: ∠2=54°.
Mathematics
Geometry
With ℓ ∥ m, ∠1=52°. Find alternate interior ∠2.<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><line x1="25" y1="48" x2="235" y2="48" stroke="#1f2937" stroke-width="2"/><line x1="25" y1="132" x2="235" y2="132" stroke="#1f2937" stroke-width="2"/><line x1="75" y1="15" x2="170" y2="165" stroke="#2563eb" stroke-width="2.5"/><text x="95" y="42" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">∠1</text><text x="144" y="125" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">∠2</text><text x="25" y="23" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">ℓ ∥ m</text></svg>
A. 68°
B. 60°
C. 52°
D. 44°
Correct Answer: C
Alternate interior angles are equal: ∠2=52°.
Mathematics
Geometry
With ℓ ∥ m, ∠1=50°. Find alternate interior ∠2.<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><line x1="25" y1="48" x2="235" y2="48" stroke="#1f2937" stroke-width="2"/><line x1="25" y1="132" x2="235" y2="132" stroke="#1f2937" stroke-width="2"/><line x1="75" y1="15" x2="170" y2="165" stroke="#2563eb" stroke-width="2.5"/><text x="95" y="42" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">∠1</text><text x="144" y="125" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">∠2</text><text x="25" y="23" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">ℓ ∥ m</text></svg>
A. 50°
B. 42°
C. 58°
D. 66°
Correct Answer: A
Alternate interior angles are equal: ∠2=50°.