**Favorite Math Problem**

Problem solving encourages critical thinking and allows students to gain value from applying concepts and skills by not being directly taught the methodology. As a future mathematics teacher, utilizing problem solving for the young to master techniques to approach real life mathematics is of overall importance. Students should understand what justifies mathematics and problem solving is one of them.

The following is a mathematical problem connected to the core curriculum and can be utilized in geometry and algebra.

The following is a mathematical problem connected to the core curriculum and can be utilized in geometry and algebra.

**Proof Through Geometry**

The figure shows an equilateral triangle ABC with DE parallel to BC and EF parallel to AB. D and G are on AB; F and H are on BC. GM and HN are perpendicular to AC. If AC = a, DG = d, FH = f, and MN = x prove that x = (a + d + f) / 2

Equilateral Triangle ABC

AC = a

DE // BC, EF // AB

DG = d

FH = f

GM perpendicular to AC

HN perpendicular to AC

**Given:**Equilateral Triangle ABC

AC = a

DE // BC, EF // AB

DG = d

FH = f

GM perpendicular to AC

HN perpendicular to AC

**Prove:**

x=(a+d+f)/2