Question

what is the term for a triangle with one interior angle measuring more than 90 degrees?
a. right triangle
b. acute triangle
c. obtuse triangle
d. equilateral triangle

what is the center of the circle inscribed in a triangle called?
a. incenter
b. orthocenter
c. centroid
d. circumcenter

a triangle is formed by three streets intersecting at points a, b, and c. to find the best location for a fire station equidistant from all three streets, you would use the:
a. circumcenter
b. centroid
c. orthocenter
d. incenter

what is the point called where the perpendicular bisectors of the sides of a triangle meet?
a. orthocenter
b. centroid
c. incenter
d. circumcenter

which point of concurrency is equidistant from all three vertices of a triangle?
a. centroid
b. circumcenter
c. orthocenter
d. incenter

which point of concurrency is equidistant from all three sides of a triangle?
a. circumcenter
b. orthocenter
c. centroid
d. incenter

Explanation:

• First question:
• A right - triangle has one angle equal to \(90^{\circ}\).
• An acute triangle has all angles less than \(90^{\circ}\).
• An obtuse triangle has one angle greater than \(90^{\circ}\).
• An equilateral triangle has all angles equal to \(60^{\circ}\).
• Second question:
• The incenter is the center of the inscribed circle in a triangle.
• The orthocenter is the intersection of the altitudes of a triangle.
• The centroid is the intersection of the medians of a triangle.
• The circumcenter is the center of the circumscribed circle around a triangle.
• Third question:
• The incenter is equidistant from all three sides of a triangle.
• The circumcenter is equidistant from the vertices.
• The centroid divides the medians in a \(2:1\) ratio.
• The orthocenter is related to the altitudes.
• Fourth question:
• The circumcenter is the point where the perpendicular bisectors of the sides of a triangle meet.
• The orthocenter is related to altitudes.
• The centroid is related to medians.
• The incenter is related to angle bisectors.
• Fifth question:
• The circumcenter is equidistant from all three vertices of a triangle.
• The centroid is related to medians.
• The orthocenter is related to altitudes.
• The incenter is related to sides.
• Sixth question:
• The incenter is equidistant from all three sides of a triangle.
• The circumcenter is equidistant from vertices.
• The centroid is related to medians.
• The orthocenter is related to altitudes.

Answer:

1. c. Obtuse Triangle
2. a. Incenter
3. d. Incenter
4. d. Circumcenter
5. b. Circumcenter
6. d. Incenter