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Question 6 • Math 3

In which figure is point cap g an orthocenter?

Answer

Image with description Triangle D F E has D at the top, F at the lower left, and E at the lower right. A marked point lies on each side. The two parts of side D F have matching single tick marks, and the two parts of side D E have matching single tick marks. The two parts of side F E have matching double tick marks. Three interior segments meet at point G: one from D to the marked point on F E, one from F to the marked point on D E, and one from E to the marked point on D F.

Image with description Triangle A B C has A at the upper left, C at the lower left, and B at the lower right. A right-angle marker is shown at C. Three interior segments intersect at point G: one from A to side C B, one from B to side A C, and one from C to side A B.

Image with description Triangle L M N has L at the upper left, M at the lower left, and N at the right. Three interior segments meet at point G: one from L to side M N, one from M to side L N, and one from N to side L M. At L, matching single arc marks are shown on the two angles formed by the segment from L. At M, matching double arc marks are shown on the two angles formed by the segment from M. At N, matching triple arc marks are shown on the two angles formed by the segment from N.

Image with description Triangle J H K has J at the upper left, H at the lower left, and K at the right. Three interior segments meet at point G: one from J to side H K, one from H to side J K, and one from K to side J H. A right-angle marker is shown where each segment meets the opposite side.

Explanation

An orthocenter is the point where a triangle’s three altitudes meet. An altitude runs from a vertex perpendicular to the opposite side. In figure C, each of the three segments meets the opposite side at a right angle, so they are altitudes and meet at G. Figure B shows angle bisectors, not altitudes.

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