LESSON 5 2 BISECTORS IN TRIANGLES OBJECTIVE To

LESSON 5 -2 BISECTORS IN TRIANGLES OBJECTIVE: To use properties of perpendicular bisectors & angle bisectors

The distance from a point to a line is the length of the perpendicular segment from the point to the line. YES, DISTANCE NO, NOT

THEOREM 5 -2 PERPENDICULAR BISECTOR THEOREM If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment. IF THEN

THEOREM 5 -3 PERPENDICULAR BISECTOR THEOREM (Converse) If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment. THEN IF A A

Example 1: Find CA and DB. Explain. CA = 5 cm DB = 6 cm C 5 cm A B 6 cm D REASON: C and D are on the perpendicular bisector of AB

THEOREM 5 -4 ANGLE BISECTOR THEOREM If a point is on the bisector of an angle, then it is equidistant from the sides of the angle. . THEN IF

THEOREM 5 -5 ANGLE BISECTOR THEOREM (Converse) If a point is in the interior of an angle and is equidistant from the sides of the angle, then the point is on the angle bisector. IF THEN

Example #2 Find the value of x. Then find FA and FE. 5 x = 2 x + 24 3 x = 24 x=8 FA = 5(8) = 40 C B D E A 5 x F 2 x + 24

C B FA = FE Why? D E A 5 x F 2 x + 24 A point on an angle bisector is equidistant from the sides of the angle.

ASSIGNMENT: Page 251 #1 -26, 41 -42, 55 -57 Write algebraic equations for #6, 7, 9, 55, 56, 57 Write out the thms for 5, 8, 17, 26