Mathematics

Mathematics

Problem

In △XYZ\triangle XYZ, let LL, MM and NN be the midpoints of sides XYXY, YZYZ and ZXZX respectively. a. (i) Prove that LM∥XZLM \parallel XZ, MN∥XYMN \parallel XY and NL∥YZNL \parallel YZ. b. (ii) Show that △LMN\triangle LMN is similar to △XYZ\triangle XYZ. c. (iii) Prove that the area of △LMN\triangle LMN is one–quarter of the area of △XYZ\triangle XYZ.

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