Relationships of Triangles: Congruence — Test

Question 7 • Geometry

In the diagram, which must be true for point cap d to be an orthocenter?

Answer

line segment BE is a perpendicular bisector of line segment AC , line segment CF is a perpendicular bisector of line segment AB , and line segment AG is a perpendicular bisector of line segment BC .

line segment BE bisects line segment AC , line segment CF bisects line segment AB , and line segment AG bisects line segment BC .

line segment BE , line segment CF , and line segment AG are angle bisectors.

line segment BE perpendicular to line segment AC , line segment AG perpendicular to line segment BC , and line segment CF perpendicular to line segment AB .

Explanation

An orthocenter is the point where a triangle’s three altitudes intersect. Each altitude passes through a vertex and is perpendicular to the opposite side, so BE must be perpendicular to AC, AG to BC, and CF to AB. These are exactly the conditions in choice D.

AI-written and checked against the verified answer.

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