Given: BE and AD are altitudes (intersecting at H) of triangle ABC, while F, G, and K are midpoints of AH, AB and BC, respectively. Prove: angle FGK is a right angle.

Solution :

Since is an altitude of a triangle , it is perpendicular to (since the triangle ).

Since and are the midpoints, then the line and the line . The line must be parallel to the line and is therefore perpendicular to

Now since F and are the mid points, we get  . The line is parallel to BH  and is perpendicular to AC.

Therefore, we have

parallel to

perpendicular to

parallel to

Thus is perpendicular to and also ∠ is a right angle.

-2x + 7 = 7

subtract 7 from both sides.

-2x = 0

divide both sides by -2.

x = 0

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step-by-step explanation:

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