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Special Triangle Points Quiz

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Special Triangle Points Quiz

Solve each challenge about the four special points of a triangle. Use precise geometry vocabulary and show your reasoning where asked.

Identify the points

A triangle’s special points are formed by intersecting medians, lines perpendicular to sides at their midpoints, lines that divide angles equally, and lines through vertices perpendicular to the opposite sides.

1.Which point is where the three medians of a triangle intersect?
  • Circumcenter
  • Incenter
  • Centroid
  • Orthocenter
2.The point equidistant from all three vertices is the .
3.Which lines intersect to form the incenter?
  • Medians
  • Perpendicular bisectors
  • Lines that divide angles into two equal angles
  • Altitudes
4.Match each line type to its definition.
  • Median
  • Altitude
  • Perpendicular bisector
  • Angle bisector
  • Passes through a vertex and is perpendicular to the line containing the opposite side
  • Splits an angle into two equal angles
  • Cuts a side in half at a right angle
  • Connects a vertex to the midpoint of the opposite side

Investigate triangle centers

Use what you know about the shape of a triangle to predict where its special points lie.

5.Sketch an obtuse triangle. Mark its four special points: the intersections of the medians, interior angle bisectors, perpendicular bisectors, and altitudes. Which two of the four points must be outside the triangle?
6.A right triangle has hypotenuse endpoints P and Q. Where is the center of the circle that passes through all three vertices located?
7.The centroid G is (4, 6). Two vertices of a triangle are A(2, 3) and B(8, 9). Find the coordinates of the third vertex C. Use the fact that the centroid is the average of the vertex coordinates.
8.The centroid divides every median into two parts. From the vertex to the centroid is 8 cm. How long is the section from the centroid to the midpoint of the opposite side?
9.A circular safety zone is drawn around a triangular rock pool so that its edge passes through all three corners. The center of the circle is 7 feet from one corner. How far is it from each of the other two corners, and what is the name of this triangle center?
10.Explain why the incenter is always inside a triangle. Include what the incenter is equidistant from.
11.True or false: The orthocenter is the point where the three perpendicular bisectors meet. If false, correct the statement.
TrueFalse

3 printable pages

  • Special Triangle Points Quiz, page 1 of 3: Identify the points

    Page 1

  • Special Triangle Points Quiz, page 2 of 3: Investigate triangle centers

    Page 2

  • Special Triangle Points Quiz, page 3 of 3: 10. Explain why the incenter is always inside a triangle. Include what the incenter is…

    Page 3

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