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Question

In triangle XYZ, A is the midpoint of XY, B is the midpoint for YZ, and C is the midpoint of XZ. Also, AY = 7 BZ = 8 XZ = 18 What Is the perimeter of Triangle ABC? SHOW ALL WORK WILL GIVE BRAINLIEST

Answer

The perimeter of triangle ABC is 24 cm. Step-by-step explanation: In triangle XYZ, point A is the midpoint of side XY, point B is the midpoint of side YZ, and point C is the midpoint of side XZ. The length of side AY is 7 cm, the length of side BZ is 8 cm, and the length of side XZ is 18 cm. According to the mid-point theorem, the line segment connecting two midpoints of a side of a triangle is parallel to the third side and half as long. Applying this theorem, we can determine the lengths of sides BC, AC, and AB. Since AY = 7 cm and A is the midpoint of XY, BC is parallel to XY and half as long. Therefore, BC = 7 cm. Since BZ = 8 cm and B is the midpoint of YZ, AC is parallel to YZ and half as long. Therefore, AC = 8 cm. Since XY = 18 cm and A and B are midpoints of sides XY and YZ, respectively, AB is parallel to XZ and half as long. Therefore, AB = 9 cm. Finally, we can find the perimeter of triangle ABC by adding the lengths of its three sides: 7 cm + 8 cm + 9 cm = 24 cm.