Question

5. Given a triangle ABC, let M be the midpoint of the segment AB. The segment CM is called the median of the triangle. Let T be the point on the line AB such that CT is perpendicular to AB (that is, T is the foot of the perpendicular dropped from C to AB). The segment CT is called the altitude of the triangle. (a) Construct a triangle ABC given two segments congruent to the sides AB and BC, respectively, and a segment congruent to the altitude CT. (8 points) (b) Construct a triangle ABC given two segments congruent to the sides AC and BC, respectively, and a segment congruent to the altitude CT. (8 points) (c) Construct a triangle ABC given two segments congruent to the sides AB and BC, respectively, and a segment congruent to the median CM. (6 points) (d) Construct a triangle ABC given two segments congruent to the sides AC and BC, respectively, and a segment congruent to the median CM.1 (12 points)

hint for d): consider a point D such that M is the midpoint of CD. Which segments are congruent here? Do you see a triangle with all three side lengts given.

Could you please write some instructions on the side so I know how to follow your solution?

Answer 1

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