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Summary 5.1 Bisectors Of Triangles (Circumcenter (Acute Triangle f…
Summary 5.1 Bisectors Of Triangles
Vocabulary
Concurrent line: when three or more lines intersect at a common point.
Point of concurrency: point of intersection in a concurrent line.
Locus: Is a set points that satisfies a particular condition.
Circumcenter: is a point of intersection of perpendicular bisectors of a triangle only
Theorems
Perpendicular Bisector Theorem
If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.
Converse Perpendicular Bisector Theorem
If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment.
Circumcenter Theorem
The perpendicular bisectors of a triangle intersect at a point called the circumcenter that is equidistant from the vertices of the triangle.
Angle Bisector Theorem
If a point is on the bisector of an angle, then it is equidistant from the sides of an angle.
Converse Angle Bisector Theorem
If a point in the interior of an angle is equidistant from the sides then it is a bisector.
Incenter theorem
The angle bisectors of a triangle intersect at a point called the incenter that is equidistant from the sides of the triangle.
Example
YZ=22.4
WZ=25.3
XY=22.4
WX= 25.3
Circumcenter
Acute Triangle
Inside
Obtuse Triangle
Outside
Right Triangle
On hypotenese
.
Locations:
Point of intersection of perpendicular bisectors
Sides are bisected
From vertex to circumcenter are congruent
Angles are not bisected
Perpendicular lines are not congruent
Angle bisector lines are not congruent
Incenter
Point of intersection of angle bisectors
From vertex to circumcenter are not congruent
Sides are not bisected
Angle bisector lines are congruent
Perpendicular lines are congruent
Angles are bisected
Lean Alsuwailem
.
Nouf Alhedeithy
Aljohara Jamalaldeen
Alya Almanea
