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In the given figure below, a segment joins the midpoints of two sides of a triangle. Find the values of x and y.
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| Photo by Math Principles in Everyday Life |
Solution:
Consider the given figure above
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| Photo by Math Principles in Everyday Life |
There are two variables in the given figure which are the sides of a big triangle. We need two equations in order to solve for the values of x and y.
Since a line segment joins the midpoints of two sides of a triangle, then the first working equation is
A small triangle is similar to big triangle because a line segment which is its base that joins the midpoints of two sides of a big triangle is parallel to the base of big triangle. By similar triangles, the second working equation is
but
Therefore, the value of x is
and the value of y is
