Points of Concurrency Review

When you draw the perpendicular bisectors of a triangle it creates the point of concurrency called the _____________.

• Centroid

• Incenter

• Circumcenter

• Orthocenter

Answer explanation

When you draw the perpendicular bisectors of a triangle, they intersect at the circumcenter, which is the center of the circle that can be circumscribed around the triangle. Thus, the correct answer is Circumcenter.

When you draw the medians of a triangle it creates the point of concurrency called the _____________.

• Centroid

• Incenter

• Orthocenter

• Altitude

Answer explanation

When you draw the medians of a triangle, they intersect at a point called the centroid. The centroid is the center of mass and divides each median into a 2:1 ratio, making it the correct answer.

The figure is an example of a(n) ...

• altitude 

• perpendicular bisector

• median

• angle bisector

Answer explanation

The figure represents a perpendicular bisector, which is a line that divides a segment into two equal parts at a right angle. This distinguishes it from altitudes, medians, and angle bisectors.

C is the Centroid, AB = 30, AC = ?

• 10

• 15

• 20

• 5

Answer explanation

In a triangle, the centroid divides each median in a 2:1 ratio. Given AB = 30, AC must be 20 to maintain this ratio, as the centroid C is closer to A than to B.

Where is the circumcenter located in an obtuse triangle?

• inside triangle

• outside triangle

• on the right angle

• on the hypotenuse

Answer explanation

In an obtuse triangle, the circumcenter, which is the point where the perpendicular bisectors of the sides intersect, lies outside the triangle. This is because the obtuse angle pushes the circumcenter away from the triangle.

Where is the orthocenter located in a right triangle?

• inside triangle

• outside triangle

• on the right angle

• on the hypotenuse

Answer explanation

In a right triangle, the orthocenter is located at the vertex of the right angle. This is because the altitudes from the other two vertices meet at this point, making the correct answer 'on the right angle'.

Segment AD is ________.

• a perpendicular segment

• a median 

• an angle bisector

• an altitude

Answer explanation

Segment AD is an angle bisector because it divides the angle into two equal parts. This distinguishes it from other options like median, altitude, or perpendicular segment, which serve different geometric purposes.

Which point of concurrency is this?

• Circumcenter

• Orthocenter

• Incenter

• Centroid

Answer explanation

The incenter is the point where the angle bisectors of a triangle intersect. It is equidistant from all sides of the triangle, making it the correct answer for this question.

The three altitudes of a triangle intersect at the___________________.

• orthocenter

• incenter

• centroid

• circumcenter

Answer explanation

The three altitudes of a triangle intersect at the orthocenter. This point is where all three altitudes meet, making it the correct answer among the given choices.

The incenter of a triangle is equidistant from the __________ of a triangle.

• vertices

• sides

• angle bisector

• circumcenter

Answer explanation

The incenter of a triangle is the point where the angle bisectors intersect, and it is equidistant from the sides of the triangle. This property defines the incenter, making 'sides' the correct answer.