Geometry Honors B ISECTORS IN T RIANGLES. Vocabulary Perpendicular Bisector – a line, a segment, or a ray that is perpendicular to a segment at its midpoint.

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Presentation transcript:

Geometry Honors B ISECTORS IN T RIANGLES

Vocabulary Perpendicular Bisector – a line, a segment, or a ray that is perpendicular to a segment at its midpoint.

Theorem Perpendicular BisectorTheorem- If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.  

Theorem Converse of the Perpendicular Bisector Theorem- If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment. 

Vocabulary Distance from a point to a line– the length of the perpendicular segment from the point to the line. 

Theorem Angle BisectorTheorem- If a point is on the bisector of an angle, then the point is equidistant from the sides of the angle. 

Theorem Converse of the Angle Bisector Theorem- If a point in the interior of an angle is equidistant from the sides of the angle, then the point is on the angle bisector. 

Application of Theorems X W Y Z V How is WY related to XZ?

Application of Theorems X W Y Z V Find XV, WZ and XY.

Application of Theorems X W Y Z V What kind of Triangle is  WXV?

H K J I Application of Theorems 3x + 2 4x - 3 Find the value of x. Find HI and JI. If L lies on KI, then L is ________ from H and J. What kind of triangle is  HIJ?

Q S P R Application of Theorems 6y 8y - 7 Find the value of y. Find PS and RS. What kind of triangle is  PQS?

H OMEWORK