Unit 1 - Introduction to Geometry - Thereoms

Question 1

Definition of the Perpendicular Bisector Theorem

Answer 1

1. A point found on the Perpendicular Bisector
2. Always is equidistant from the endpoints of a line segment

Question 2

Definition of the Circumcenter Theorem

Answer 2

The circumcenter is equidistant to the triangle’s three vertices.

Question 3

Definition of the Angle Bisector Theorem

Answer 3

If a point is on the bisector of an angle, then it is equidistant from sides of an angle

(measuring distance must be done perpendicularly)

Question 4

Definition of Isosceles Triangle Theorem

Answer 4

If two sides of a triangle are congruent, then the angles opposite of those sides are congruent.

Question 5

Definition of Converse of Isosceles Triangle Theorem

Answer 5

If two angles of a triangle are congruent, then the sides opposite those angles are congruent.

Question 6

How does the Circumcenter Theorem connect with a circumscribed circle?

Answer 6

1. The radii of the circle represents how the vertices are equidistant from the circumcenter.
2. The vertices are all radii because they all touch the edge of the circle.
3. The distance from the circumcenter and the edge of the circle will always be equal no matter where the edge is.
4. That is why all radii, including the distances between the radii and the circumcenter, are all equal to each other.

Question 7

Definition of the Incenter Thereom

Answer 7

The incenter is equidistant from each side of the triangle.

Question 8

How does the Incenter Theorem connect with a inscribed circle.

Answer 8

1. The radii of the circle represents how the sides are equidistant from the incenter.
2. The sides are all radii because they all touch the edge of the circle.
3. The distance from the incenter and the edge of the inscribed circle will always be equal no matter the location.
4. That is why all radii, including the distances between the radii and the incenter, are all equal to each other.