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Discovery Lab 1: Centers of a triangle

Auteur :ssvestal

Incenter of a triangle

Construct an acute triangle in the window below. Construct the angle bisectors of each angle. From doing this activity with patty paper, we know that the angle bisectors intersect in a point when the triangle is acute. Now pick one of the vertices of the triangle and change the shape of the triangle so that the triangle is obtuse.

Intersection of angle bisectors

Do the angle bisectors still intersect at one point if the triangle is obtuse?

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  • B
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Location of point of intersection

Do the angle bisectors intersect inside the triangle when the triangle is obtuse?

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  • B
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Incenter of a right triangle

Now manipulate your triangle until it is a right triangle. What happens to the point of intersection of the angle bisectors when the triangle is a right triangle?

Circumcenter of a triangle

Construct an acute triangle in the window below. Construct the perpendicular bisectors of each side of the triangle. From doing this activity with patty paper, we know that the perpendicular bisectors intersect at a point inside the triangle when the triangle is acute. Now pick one of the vertices of the triangle and change the shape of the triangle so that the triangle is obtuse.

Do the perpendicular bisectors still intersect at one point if the triangle is obtuse?

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  • A
  • B
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Location of intersection

Do the perpendicular bisectors intersect inside the triangle when the triangle is obtuse?

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  • A
  • B
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Circumcenter of a right triangle

Now manipulate your triangle until it is a right triangle. What happens to the point of intersection of the perpendicular bisectors when the triangle is a right triangle?

Centroid of a triangle

Construct an acute triangle in the window below. Construct the medians of the triangle. From doing this activity with patty paper, we know that the medians intersect at a point inside the triangle when the triangle is acute. Now pick one of the vertices of the triangle and change the shape of the triangle so that the triangle is obtuse.

Location of intersection

Do the medians intersect inside the triangle when the triangle is obtuse?

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  • A
  • B
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Centroid of a right triangle

Now manipulate your triangle until it is a right triangle. What happens to the point of intersection of the medians when the triangle is a right triangle?

Orthocenter of a triangle

Construct an acute triangle in the window below. Construct the altitudes of the triangle. From doing this activity with patty paper, we know that the altitudes intersect at a point inside the triangle when the triangle is acute. Now pick one of the vertices of the triangle and change the shape of the triangle so that the triangle is obtuse.

Do the altitudes intersect inside the triangle when the triangle is obtuse?

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  • A
  • B
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Orthocenter of a right triangle

Now manipulate your triangle until it is a right triangle. What happens to the point of intersection of the altitudes when the triangle is a right triangle?

Comparing Discovery Lab 1 with patty paper and with Geogebra

In the box below, list the advantages and disadvantages of Discovery Lab 1 with patty paper and with Geogebra. Which was your preference? Which would you be more likely to use in your classroom.

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