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1. Match the picture of the triangle to the correct name for its center,

1. Match the picture of the triangle to the correct name for its center,-example-1
User Natty
by
2.7k points

2 Answers

29 votes
29 votes

Answer:

1. d 2. a 3. c 4. b

Explanation:


1.d\ \{The\ intersection\ of\ three\ high\ lines\}


2.\ a


3.\ C


4.\ b\ \{The\ intersection\ of\ three\ angular


bisectors\}

I hope this helps you

:)

User Mathias Brossard
by
3.1k points
29 votes
29 votes

Answer:

  1. d
  2. b
  3. c
  4. a

Explanation:

Various centers are defined for a triangle, depending on how they're constructed. Here, you're asked to match the construction with the name.

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Orthocenter

The orthocenter is the intersection of the altitudes of the triangle. Each altitude intersects a vertex and is orthogonal to the opposite side. The orthocenter will not be inside the triangle if the triangle is obtuse. The orthocenter of a right triangle is the right-angle vertex.

Figure D depicts the intersection of altitudes.

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Incenter

The incenter is the center of an inscribed circle of a triangle. The incenter must be the same distance from each side, so will be at the point of intersection of the angle bisectors. It always lies inside the triangle.

Figure B depicts the intersection of angle bisectors.

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Centroid

The centroid is the "center of gravity" of the triangle, the point at which the triangle could be balanced. Each median divides the triangle into two equal areas, so the intersection of medians marks a spot with equal area (weight) in every pair of opposite directions.

Figure C depicts the intersection of medians.

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Circumcenter

The circumcenter is the center of a circle that circumscribes the triangle. It is equidistant from the three vertices, so lies on the intersection of the perpendicular bisectors of the sides. It will lie outside the triangle for obtuse triangles. It is the midpoint of the hypotenuse of a right triangle.

Figure A depicts the intersection of perpendicular bisectors of the sides.

User Lajara
by
2.9k points