Unit 8

Question 1

Parallel Lines Intercept Equal Segments Theorem

Answer 1

If a transversal cuts a set of parallel lines into x amount of equal segments, then another transversal will cut the same set of parallel lines into that same amount of equal segments.

Question 2

Centroid To Vertex Theorem

Answer 2

The distance from the centroid to the vertex is 2/3 of the median.

Question 3

Right Triangle Theorem

Answer 3

If ABC is a right triangle, then the midpoint of the hypotenuse is the circumcenter.

Question 4

Right Triangle Theorem Corollary

Answer 4

If ABC is a 30-60-90 triangle, then the hypotenuse is twice the side opposite the 30 degree angle.

Question 5

Right Triangle Theorem Corollary Converse

Answer 5

If in right triangle ABC the hypotenuse is twice a leg, then the angle opposite that leg is 30 degrees.

Question 6

Right Triangle 2nd Theorem

Answer 6

If the midpoint of one side of a triangle is equidistant from all three vertices, then the angle opposite that side is a right angle.

Question 7

What is the Euler segment?

Answer 7

The Euler segment connects the orthocenter with the circumcenter, passing through the centroid. The circumcenter and orthocenter are always the endpoints.

Question 8

Euler segment extension

Answer 8

The distance from the orthocenter to the centroid is 2/3 of the Euler segment. The distance from the circumcenter to the centroid is 1/3 of the Euler segment.