An isosceles right-angled triangle DEF is inscribed in triangle ABC so that its hypotenuse DF is parallel to AC.

| September 26, 2021 | education

An isosceles right-angled triangle DEF is inscribed in triangle ABC so that its hypotenuse DF is parallel to AC. Find the height of the triangle ABC, drawn from the vertex B, if AC = 16 cm and DF = 8 cm

Since, according to the condition, the length of the segment DF is equal to half the length of the base of the AC and DF is parallel to the AC, then the segment DF is the midline of the triangle ABC.

BH is the height of triangle ABC, which the middle line DF divides in half, according to the property of the middle line.

Then BK = KH = BH / 2.

The DFE triangle is rectangular, HK is its height, which divides DF in half, which means it is the median. Then the triangle DFE is also isosceles, then the angle HDK = HFK = 45.

Then KH = DK = DF / 2 = 4 cm.

BH = 2 * KH = 8 cm.

Answer: The height of the triangle ABC is 8 cm.



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