chapter 5 congruent triangles. 5.1 perpendiculars and bisectors perpendicular bisector: segment,...
TRANSCRIPT
5.1 Perpendiculars and Bisectors Perpendicular Bisector: segment, line, or
ray that is perpendicular and cuts a figure into two parts
Equidistant: same distance away Distance from Point to Line: the space
between a point and a line
Perpendicular Bisector Theorem:If a point is on a perpendicular bisector, then it is equidistant from the segment endpoints.
Converse of Perpendicular Bisector Theorem:If a point is equidistant from the segment endpoints, then the point is on the perpendicular bisector.
Angle Bisector Theorem: If a point is on an angle bisector, then it is equidistant from the sides of the angle
Converse of Angle Bisector Theorem:If a point is equidistant from the sides of an angle, then it lies on the angle bisector.
Checkpoint
Point Q will be on the perpendicular bisector QS
No, you don’t know any equal lengths of sides PS and RS
5.2 Perpendiculars and Bisectors Perpendicular Bisector of a Triangle: segment
from the midpoint of each side extended perpendicular to the interior of the triangle
Concurrent Lines: lines that intersect in one point
Circumcenter: point where all perpendicular bisectors intersect
Angle Bisector: ray that divides the angle in half
Pythagorean Theorem: a2 + b2 = c2, where “c” is the hypotenuse
5.2 Continued Incenter: point where all angle bisectors
intersect Perpendicular Bisector Theorem: the circumcenter is equal distance away from the three vertices
5.2 Continued Angle Bisector Theorem: the incenter is
equal distance from the sides of the triangleMeasured perpendicular to the sides
Example 1: Using Perpendicular Bisectors
Find the perpendicular bisectors of each side of the triangle. The concurrent point (circumcenter) is the equidistant buoy
Example 2: Using Angle Bisectors
HM = HN = HP because of incenter
Pythagorean Theorem now has to be used to find missing lengths