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* In geometry, Stewart's Theorem is named in honor of the Scottish mathematician Matthew Stewart. He published this theorem in 1746. It is also known as "Proposition II" in Stewart's book Some General Theorems of Considerable Use in the Higher Parts of Mathematics. * * Stewart's theorem yields a relation between the lengths of the sides of the triangle and the length of a cevian of the triangle. * A cevian is a line segment or ray that extends from one vertex of a polygon to the opposite side (or the extension of that side). Medians, altitudes, and angle bisectors are all examples of cevians. * The theorem helps find the measure of any line segment from the vertex of a triangle to the opposite side. * The theorem is established from Cosines law. A man + dad = bmb + cnc b c “A man and his dad put a bomb in the sink” d B m n D a C A 4 x 3 B 3 D 2 C In right ∆ABC, AB is 4cm, AC is 3cm, BD is 3 cm, and DC is 2cm. Using Stewart’s Theorem, what is the value of x? E Isosceles ∆EFG has a leg measure of 10in. FH has 2in and HG has 6in. Find x. 10 x F 2 H 6 G *