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McGraw Hill Integrated II, 2012 View details

2. Medians and Altitudes of Triangles

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Exercise 30 Page 423

Use the definition of an altitude and the Converse of the Perpendicular Bisector Theorem.

Altitude, perpendicular bisector

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We are given that LM is perpendicular to JK. Let's mark this on the given diagram.

According to the definition, an altitude of a triangle is a segment from a vertex to the line containing the opposite side and perpendicular to the line containing that side. From the diagram, we can see that LM is a segment from the vertex L to the opposite side JK and is perpendicular to JK. Thus, LM is an altitude of △ JLK.

Also, we are told that segments JL and KL are congruent. This tells us that point L is equidistant from J and K. Now we can use the Converse of the Perpendicular Bisector Theorem.

If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment.

By this theorem, L lies on the perpendicular bisector of the segment. We conclude that LM is also a perpendicular bisector of △ JLK.

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Exercises p.421-425

Exercise 30 Page 423

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