Download - 1 - Geometry Honors Chapter 5 Constructions Worksheet Name

Geometry Honors Chapter 5 Constructions Worksheet
Name _________________________________
Honor Code: ______________________________________________________________________________________
1.
Construct the perpendicular bisectors of each of the following triangles. Label the point of concurrency of the
perpendicular bisectors P and answer the following questions.
Acute Triangle
Right Triangle
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Obtuse Triangle
Properties of the perpendicular bisector:

A perpendicular bisector is a segment, ray, line, or plane that is perpendicular to a segment at its _____________.

The point of concurrency (intersection) of a triangle's perpendicular bisectors is called the ___________________.

The circumcenter is equidistant from all three ___________________ of the triangle.

The circumcenter is the center of the ____________________ circle, which can be constructed through all three
vertices.

In a right triangle, the circumcenter is also the ___________________ of the hypotenuse.

In an acute triangle, the circumcenter is located __________________ the triangle.

In an obtuse triangle, the circumcenter is located __________________ the triangle.
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2.
Construct the angle bisectors of each of the following triangles. Label the point of concurrency of the angle bisectors
P and answer the following questions.
Acute Triangle
Right Triangle
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Obtuse Triangle
Properties of the angle bisector:

An angle bisector _____________ a vertex angle.

The point of concurrency (intersection) of the three angle bisectors is called the ______________________.

The incenter is equidistant from the three _________________ of the triangle.

The incenter is the center of the circle that can be _____________________ inside the triangle.

The incenter is always located ____________________ of the triangle.

An angle bisector will intersect the opposite side, but it may or may not go through the midpoint.
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3. Construct the medians of each of the following triangles. Label the point of concurrency of the medians P and answer
the following questions.
Acute Triangle
Right Triangle
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Obtuse Triangle
Properties of the median:

A median passes through a vertex of the triangle and the __________________ of the opposite side.

The intersection of the three medians is called the __________________.

The distance from the vertex to the centroid is ______________ the length of the median.

The distance from the centroid to the side midpoint is ____________ the length of the median.

The centroid is the center of ___________________ of a triangle.

In acute, right, and obtuse triangles, the centroid is located _________________ the triangle.

A median passes through a vertex, but may or may not bisect the angle.
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4. Construct the altitudes of each of the following triangles. Label the point of concurrency of the altitudes P and answer
the following questions.
Acute Triangle
Right Triangle
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Obtuse Triangle
Properties of the altitude:

An altitude passes through a vertex and is ___________________ to the opposite side.

The intersection of the altitudes is called the _______________________

In an acute triangle, the orthocenter is located _______________ the triangle.

In an obtuse triangle, the orthocenter and two of the altitudes are located __________________ of the triangle.

In a right triangle, the orthocenter falls on the _____________________ of the right angle and the two legs are
also altitudes.
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