Special Segments
Name That Center
Inside or Outside
Circles and Construction
Challenge Round
100

This special segment connects a vertex of a triangle to the midpoint of the opposite side.

What is a median

100

Three medians meet at this triangle's center.

What is the centroid?

100

True or false: The centroid is always inside a triangle.

What is true?

100

This tool is used to draw circles during geometric constructions.

What is a compass?

100

An angle measures 80°. An angle bisector divides it into two angles of this measure.

What is 40°?

200

This special segment divides an angle into two equal angles.

What is an angle Bisector?

200

Three angle bisectors meet at this triangle center.

What is the incenter?

200

This triangle center, made by angle bisectors, is always inside a triangle.

Incenter

200

A circle that touches all three sides of a triangle is called this.

What is an incircle (inscribed circle)?

200

A median divides a side of a triangle into two parts. One part measures 7 cm. This is the length of the whole side.

What is 14 cm?

300

This segment cuts a side in half and forms a 90° angle.

What is a perpendicular bisector?

300

Three altitudes meet at this triangle center.

What is the orthocenter?

300

In an obtuse triangle, the orthocenter is located here.

What is outside the triangle?

300

To construct an incircle, you first construct these special segments.

What are angle bisectors?

300

Three altitudes meet outside a triangle. The triangle must be this type.

What is an obtuse triangle?

400

This special segment starts at a vertex and forms a right angle with the opposite side.

What is an altitude?

400

Three perpendicular bisectors meet at this triangle center.

What is the circumcenter?

400

In a right triangle, the circumcenter is located here.

What is on the triangle (at the midpoint of the hypotenuse)?

400

The center of a circumcircle is this triangle center.

What is the circumcenter?

400

A perpendicular bisector divides a 16 cm side into two equal parts. Each part measures this much.

What is 8 cm?

500

A segment cuts a side into two equal parts but does not make a 90° angle. It begins at the opposite vertex. Name the segment.

What is a median?

500

This center is known as the triangle's center of gravity.

What is the centroid?

500

Name BOTH triangle centers that can be outside an obtuse triangle.

What are the circumcenter and orthocenter?

500

When constructing a circumcircle, the compass distance runs from the circumcenter to this part of the triangle.

What is a vertex?

500

A triangle has a 90° angle. Its orthocenter is located at this specific point.

What is the vertex of the right angle?