Question

Can someone please help me with problem 6 of this assignment? I included the measurements of the triangle so that you are able to solve it accurately.

Geometry Topic: 6.1 - 6.4 Constructing Parts and Centers

Problem 6 Directions: Remember! Triangle centers may be outside the triangle.  Locate the orthocenter of each triangle by finding the intersection of the altitudes.

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Answer 1

let say the 3 points that make the triangle is A-B-C, you draw a line from A to the line opposite to A, make it perpendicular. If it's not inside of the triangle, you just extend the line to make it work. Then repeat for B and C. Then you extend the perpendicular lines (altitude) and make them intersect. The intersect point is the orthocenter.

Explanation:

Then you extend the perpendicular lines (altitude) and make them intersect. The intersect point is the orthocenter.

Answer 2

see attached

Explanation:

You want to construct the orthocenter of the given triangle.

Orthocenter

The orthocenter of a triangle is the point of intersection of the altitudes. The construction of it requires construction of at least two altitudes of the triangle. This is accomplished using the "perpendicular through an external point" construction.

Perpendicular through an external point

A perpendicular to a line through a point not on the line is constructed in a few simple steps:

1. Using the external point as a center, draw an arc that intersects the line in 2 places.
2. Using each of those points as a center, draw intersecting arcs with the same radius
3. The line through that point of intersection and the original point is perpendicular to the line

The attachment shows arc FG using C as a center, and arc HI using A as a center. Arcs using those points as center are drawn so they intersect at points V and W.

Lines CV and AW are altitude lines that intersect at the orthocenter: point Z.

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Additional comment

The vertices of the original triangle have been labeled A, B, C counterclockwise from upper left.

It may appear that point Z is a reflection of point C in line AB, but it is not.