1.4 Lines, bisectors, & conjectures

1.4 Lines, bisectors, & conjectures Warm-Up: m<ABC = (35 + x)⁰, findm<DBC Objectives: Define perpendicular lines, parallel lines, segment bisectors, angle bisectors, and geometry conjectures. A D (x+6)⁰ B (2x+1)⁰ C

Vocabulary: Perpendicular Lines: Two lines that intersect to form a right angle.

Vocabulary: Parallel Lines: Two coplanar lines that do not intersect.

Vocabulary: Conjecture: A statement that is believed to be true. (an educated guess based on observations)

Vocabulary: Segment Bisector: A line that divides a segment into two congruent parts.

Vocabulary: Midpoint: The point where a bisector intersects a segment.

Vocabulary: Perpendicular Bisector: A bisector that is perpendicular to a segment.

Vocabulary: Angle Bisector: A line or ray that divides an angle into two congruent angles. D C A B

Example 1: Lines x and y are ________. Lines x and z are ________. y x z

Example 2: Note: The shortest distance from a point to a line is the measure of the segment that creates a 90⁰ angle with the line. The shortest distance from x to l is _____. A B C l x

Example 3: XY and XZ are _______ because: x line l is an angle bisector and forms a 90⁰ angle with line w. Z Y W l

Example 4: XT and XY are _______ W Y T X

Example 5: Suppose l is the perpendicular bisector of XY and that XY = 29. Find XZ and YZ. XZ = ________ YZ = ________ x l z y

Example 6: Suppose that l is the angle bisector of <ABC and that the measure of <EBC is 32. Find m<ABE and m<ABC. A m<ABE = _____ m<ABC = _____ E B l 32⁰ C

Homework: pages 39-40 #’s 5, 6, 7, 8, 25, & 26

1.4 Lines, bisectors, & conjectures