Honors GeometryPage 1

Unit 10

Using TRICENTERS.GSP

Open the file TRICENTERS.GSP from the class page. Experiment with the buttons on each of the tabs. Formulate and clarify some definitions in your exploration time.

After performing several experiments, state whether the indicated center of the triangle appears to be on a side of the triangle, in the interior of the triangle, or in the exterior of the triangle.

1.The centroid of

  1. an acute triangle_____interior______
  2. a right triangle_____interior______
  3. an obtuse triangle_____interior______

2.The circumcenter of

  1. an acute triangle_____interior______
  2. a right triangle______on______
  3. an obtuse triangle______exterior______

3.The incenter of

  1. an acute triangle_____interior______
  2. a right triangle_____interior______
  3. an obtuse triangle_____interior______

4.The orthocenter of

  1. an acute triangle_____interior______
  2. a right triangle______on______

C.an obtuse triangle______exterior______

  1. From the four points – the centroid, the circumcenter, the incenter, and the orthocenter of a triangle – select those points which appear to be in the interior region of the triangle in all triangles.

A.centroidB.circumcenter

C.incenterD.orthocenter

6.If two altitudes of a given triangle fall outside the triangle, the triangle is

A.rightB.acuteC.obtuse

7.If the point at which the perpendicular bisectors of the sides of a triangle are concurrent is outside the triangle, the triangle is

A.rightB.acuteC.obtuse

8.The altitudes of a right triangle intersect

  1. outside the triangle
  2. inside the triangle
  3. at one of the vertices of the triangle

9.The bisectors of and of intersect at point . The bisector of

  1. always passes through P.
  2. sometimes passes through P.
  3. never passes through P.

State whether each sentence is

A)Always true.S)Sometimes true.N)Never true.

If the statement is sometimes true, describe the type of triangle.

  1. The three medians of a triangle intersect at a point in the interior of the triangle.ALWAYS
  1. The three altitudes of a triangle intersect at a vertex of a triangle.

SOMETIMES

  1. The three angle bisectors of a triangle intersect at a point in the exterior of the triangle.NEVER

13. The three perpendicular bisectors of a triangle intersect at a point in the exterior of the triangle.SOMETIMES

14. The circumcenter is concurrent with a midpoint of the side of the triangle.SOMETIMES

15. All four triangle centers are collinear.SOMETIMES

16. All four triangle centers are concurrent.SOMETIMES

Complete each sentence with a word or phrase.

  1. The centroidis always between the orthocenter and the circumcenter on the Euler segment.
  1. Any point on the perpendicular bisector of a segment is equidistant from the vertices of the segment.
  1. The circumcenter of a triangle is equidistantfrom the vertices of the triangle.
  1. Any point on the angle bisector is equidistant from the sides of the angle.
  1. The incenter of a triangle isequidistant from eachsideof the triangle.
  1. The centroid of the triangle is located one - third of the distance from a vertex to the midpoint of the side opposite the vertex on a median.
  1. The intersection of the altitudes in a triangle is called the orthocenter.

TriCentersQuestions.docFricker, Evans, Cendrowski

Lower Moreland HS