Thm Prodject

Question 1

Perpendicular Bisector Theorem:

Answer 1

: If a point is on the perpendicular bisector of a segment, then it is
equidistant from the endpoints of the segment.

Question 2

Converse of the Perpendicular Bisector Theorem:

Answer 2

If a point is equidistant from the endpoints of a
segment, then it is on the perpendicular bisector of the segment.

Question 3

Angle Bisector Theorem:

Answer 3

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

Question 4

Converse of the Angle Bisector Theorem:

Answer 4

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

Question 5

ISO-BAM

Answer 5

: If a segment is a median from the vertex angle in an isosceles triangle, then it is also
the angle bisector and altitude of the triangle.z

: If a segment is the angle bisector of the vertex angle in an isosceles triangle, then it
is also the median and altitude of the triangle.

: If a segment is the altitude from the vertex angle in an isosceles triangle, then it is
also the median and angle bisector of the triangle.

Question 6

Triangle Midsegment Theorem:

Answer 6

If a segment is a midsegment of a triangle, then it is parallel to a side
of the triangle and its length is half the length of that side.

Question 7

Altitude

Answer 7

In geometry, the altitude is a line that passes through two very specific points on a triangle: a vertex, or corner of a triangle, and its opposite side at a right, or 90-degree, angle. The opposite side is called the base. All triangles have three vertices and three opposite sides.

Question 8

Midsegment

Answer 8

Midsegment Definition: The midsegment of a triangle is the segment that connects the midpoints of two sides of a triangle.

Question 9

Incentre

Answer 9

The incenter of a triangle is the intersection point of all the three interior angle bisectors of the triangle. In other words, it can be defined as the point where the internal angle bisectors of the triangle cross.

Question 10

Centroid

Answer 10

The centroid is the centre point of the object. The point in which the three medians of the triangle intersect is known as the centroid of a triangle. It is also defined as the point of intersection of all the three medians. The median is a line that joins the midpoint of a side and the opposite vertex of the triangle.

Question 11

Circumcenter

Answer 11

The circumcenter is the point where all three perpendicular bisectors of a triangle meet. The circumcenter is also the center of a circle that goes around the triangle and touches the three vertices of the triangle, which indicates that all three vertices are the same distance from the circumcenter.

2/3 s

Question 12

How to solve for Circumcenter

Answer 12

Triangle ABC
-Find midpoint AB
-Find slope of AB
-Find Opposite Reciprocal of slope and plug it in
-Find midpoint of BC
-Find Slope of BC
-Find Opposite Reciprocal of slope and plug it in
-Solve System

Question 13

How to solve for Centroid

Answer 13

Triangle ABC
-Find midpoint of AB
-Use midpoint and C to find slope between the two
-Find midpoint of BC
-Use midpoint and A to find slope
Solve system

Question 14

Orthocenter

Answer 14

A point is the orthocenter of a triangle iff it is the intersection of the lines containing the altitudes of the triangle.

Question 15

How to solve for orthocenter

Answer 15

Triangle ABC
-Find slope of AB
-Find opposite reciprocal
-plug in that slope with point C in point slope form
-Find slope of BC
-Find opposite reciprocal
-plug in that slope with point A in point slope form
-Solve system.