Mathematics
Geometry
A triangle has base 16 cm and perpendicular height 9 cm. Find its area.<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><text x="25" y="163" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">A</text><text x="225" y="163" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">B</text><text x="126" y="28" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">C</text><text x="115" y="168" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">16 cm</text><line x1="130" y1="35" x2="130" y2="145" stroke="#dc2626" stroke-width="2.5"/><rect x="130" y="135" width="10" height="10" fill="none" stroke="#dc2626"/></svg>
A. 72 cm²
B. 80 cm²
C. 68 cm²
D. 76 cm²
Correct Answer: A
Area=½bh=½×16×9=72 cm².
Mathematics
Geometry
A triangle has base 14 cm and perpendicular height 8 cm. Find its area.<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><text x="25" y="163" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">A</text><text x="225" y="163" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">B</text><text x="126" y="28" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">C</text><text x="115" y="168" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">14 cm</text><line x1="130" y1="35" x2="130" y2="145" stroke="#dc2626" stroke-width="2.5"/><rect x="130" y="135" width="10" height="10" fill="none" stroke="#dc2626"/></svg>
A. 64 cm²
B. 52 cm²
C. 56 cm²
D. 60 cm²
Correct Answer: C
Area=½bh=½×14×8=56 cm².
Mathematics
Geometry
A triangle has base 12 cm and perpendicular height 7 cm. Find its area.<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><text x="25" y="163" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">A</text><text x="225" y="163" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">B</text><text x="126" y="28" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">C</text><text x="115" y="168" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">12 cm</text><line x1="130" y1="35" x2="130" y2="145" stroke="#dc2626" stroke-width="2.5"/><rect x="130" y="135" width="10" height="10" fill="none" stroke="#dc2626"/></svg>
A. 50 cm²
B. 38 cm²
C. 46 cm²
D. 42 cm²
Correct Answer: D
Area=½bh=½×12×7=42 cm².
Mathematics
Geometry
A triangle has base 10 cm and perpendicular height 6 cm. Find its area.<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><text x="25" y="163" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">A</text><text x="225" y="163" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">B</text><text x="126" y="28" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">C</text><text x="115" y="168" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">10 cm</text><line x1="130" y1="35" x2="130" y2="145" stroke="#dc2626" stroke-width="2.5"/><rect x="130" y="135" width="10" height="10" fill="none" stroke="#dc2626"/></svg>
A. 26 cm²
B. 38 cm²
C. 34 cm²
D. 30 cm²
Correct Answer: D
Area=½bh=½×10×6=30 cm².
Mathematics
Geometry
A triangle has base 8 cm and perpendicular height 5 cm. Find its area.<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><text x="25" y="163" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">A</text><text x="225" y="163" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">B</text><text x="126" y="28" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">C</text><text x="115" y="168" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">8 cm</text><line x1="130" y1="35" x2="130" y2="145" stroke="#dc2626" stroke-width="2.5"/><rect x="130" y="135" width="10" height="10" fill="none" stroke="#dc2626"/></svg>
A. 16 cm²
B. 28 cm²
C. 24 cm²
D. 20 cm²
Correct Answer: D
Area=½bh=½×8×5=20 cm².
Mathematics
Geometry
An altitude is:<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><text x="25" y="163" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">A</text><text x="225" y="163" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">B</text><text x="126" y="28" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">C</text><line x1="130" y1="35" x2="130" y2="145" stroke="#dc2626" stroke-width="2.5"/><rect x="130" y="135" width="10" height="10" fill="none" stroke="#dc2626"/></svg>
A. Circumcenter
B. Centroid
C. Perpendicular to the opposite side
D. Median
Correct Answer: C
Correct triangle fact: Perpendicular to the opposite side.
Mathematics
Geometry
A median joins a vertex to:<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><text x="25" y="163" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">A</text><text x="225" y="163" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">B</text><text x="126" y="28" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">C</text><line x1="130" y1="35" x2="130" y2="145" stroke="#dc2626" stroke-width="2.5"/><text x="121" y="164" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">M</text></svg>
A. Centroid
B. Midpoint of opposite side
C. Circumcenter
D. Median
Correct Answer: B
Correct triangle fact: Midpoint of opposite side.
Mathematics
Geometry
A triangle with one angle above 90° is:<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><text x="25" y="163" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">A</text><text x="225" y="163" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">B</text><text x="126" y="28" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">C</text></svg>
A. Median
B. Obtuse triangle
C. Centroid
D. Circumcenter
Correct Answer: B
Correct triangle fact: Obtuse triangle.
Mathematics
Geometry
A triangle with all angles below 90° is:<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><text x="25" y="163" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">A</text><text x="225" y="163" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">B</text><text x="126" y="28" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">C</text></svg>
A. Centroid
B. Acute triangle
C. Median
D. Circumcenter
Correct Answer: B
Correct triangle fact: Acute triangle.
Mathematics
Geometry
A triangle with one 90° angle is:<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><text x="25" y="163" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">A</text><text x="225" y="163" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">B</text><text x="126" y="28" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">C</text></svg>
A. Circumcenter
B. Right triangle
C. Centroid
D. Median
Correct Answer: B
Correct triangle fact: Right triangle.
Mathematics
Geometry
Every equilateral triangle is:<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><text x="25" y="163" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">A</text><text x="225" y="163" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">B</text><text x="126" y="28" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">C</text></svg>
A. Equiangular
B. Median
C. Centroid
D. Circumcenter
Correct Answer: A
Correct triangle fact: Equiangular.
Mathematics
Geometry
Angle bisectors meet at the:<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><text x="25" y="163" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">A</text><text x="225" y="163" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">B</text><text x="126" y="28" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">C</text></svg>
A. Incenter
B. Circumcenter
C. Centroid
D. Median
Correct Answer: A
Correct triangle fact: Incenter.
Mathematics
Geometry
Perpendicular bisectors meet at the:<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><text x="25" y="163" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">A</text><text x="225" y="163" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">B</text><text x="126" y="28" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">C</text></svg>
A. None of these
B. Median
C. Centroid
D. Circumcenter
Correct Answer: D
Correct triangle fact: Circumcenter.
Mathematics
Geometry
The three altitudes meet at the:<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><text x="25" y="163" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">A</text><text x="225" y="163" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">B</text><text x="126" y="28" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">C</text><line x1="130" y1="35" x2="130" y2="145" stroke="#dc2626" stroke-width="2.5"/><rect x="130" y="135" width="10" height="10" fill="none" stroke="#dc2626"/></svg>
A. Circumcenter
B. Median
C. Centroid
D. Orthocenter
Correct Answer: D
Correct triangle fact: Orthocenter.
Mathematics
Geometry
The three medians meet at the:<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><text x="25" y="163" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">A</text><text x="225" y="163" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">B</text><text x="126" y="28" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">C</text><line x1="130" y1="35" x2="130" y2="145" stroke="#dc2626" stroke-width="2.5"/><text x="121" y="164" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">M</text></svg>
A. Median
B. Circumcenter
C. Centroid
D. None of these
Correct Answer: C
Correct triangle fact: Centroid.
Mathematics
Geometry
An isosceles triangle has vertex angle 76°. Find each base angle.<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><text x="25" y="163" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">A</text><text x="225" y="163" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">B</text><text x="126" y="28" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">C</text><text x="52" y="132" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">?</text><text x="187" y="132" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">?</text><text x="118" y="58" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">76°</text></svg>
A. 62°
B. 57°
C. 47°
D. 52°
Correct Answer: D
Base angles are equal: (180°−76°)/2=52°.
Mathematics
Geometry
An isosceles triangle has vertex angle 72°. Find each base angle.<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><text x="25" y="163" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">A</text><text x="225" y="163" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">B</text><text x="126" y="28" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">C</text><text x="52" y="132" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">?</text><text x="187" y="132" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">?</text><text x="118" y="58" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">72°</text></svg>
A. 59°
B. 64°
C. 49°
D. 54°
Correct Answer: D
Base angles are equal: (180°−72°)/2=54°.
Mathematics
Geometry
An isosceles triangle has vertex angle 68°. Find each base angle.<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><text x="25" y="163" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">A</text><text x="225" y="163" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">B</text><text x="126" y="28" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">C</text><text x="52" y="132" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">?</text><text x="187" y="132" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">?</text><text x="118" y="58" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">68°</text></svg>
A. 56°
B. 66°
C. 51°
D. 61°
Correct Answer: A
Base angles are equal: (180°−68°)/2=56°.
Mathematics
Geometry
An isosceles triangle has vertex angle 64°. Find each base angle.<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><text x="25" y="163" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">A</text><text x="225" y="163" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">B</text><text x="126" y="28" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">C</text><text x="52" y="132" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">?</text><text x="187" y="132" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">?</text><text x="118" y="58" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">64°</text></svg>
A. 63°
B. 53°
C. 68°
D. 58°
Correct Answer: D
Base angles are equal: (180°−64°)/2=58°.
Mathematics
Geometry
An isosceles triangle has vertex angle 60°. Find each base angle.<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><text x="25" y="163" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">A</text><text x="225" y="163" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">B</text><text x="126" y="28" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">C</text><text x="52" y="132" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">?</text><text x="187" y="132" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">?</text><text x="118" y="58" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">60°</text></svg>
A. 70°
B. 55°
C. 65°
D. 60°
Correct Answer: D
Base angles are equal: (180°−60°)/2=60°.