Warm-up1) What is the difference between drawing and

constructing a geometric figure?2) Draw an angle with measure of 55°

4.2 Angle Bisectors

Review:Definitions:

Angle MeasureDegreeProtractorAcute AngleRight angleObtuse angleStraight AngleCongruent Angles

Straight EdgeRulerCompassDrawSketchConstruct

Postulates4.1 Protractor Postulate4.2 Continuity Postulate

Adjacent angles are two coplanar angles that have a common side but no common interior

points.Postulate 4.3 Angle Addition Postulate. If K lies in the interior of ∠MNP. Then m∠MNP = m∠MNK + m∠KNP.

Ex #1 Find m∠XYZ if m∠XYT = 25° and m∠TYZ = 15°According to the Angle Addition Postulate :m∠XYZ = m∠XYT + m∠TYZ By substitution:m∠XYZ = (25°) + (15°)m∠XYZ = 40°

Y

X

T

Z

Ex #2 Find m∠DBC if m∠ABC = 105° and m∠ABD = 35°

According to the Angle Addition Postulate :m∠ABC = m∠ABD + m∠DBCBy substitution:(105°) = (35°) + m∠DBC - 35° -35° 70 ° = m∠DBC

B

D

A

C

An angle bisector is a ray that (except for its origin) is in the interior of an angle and forms congruent adjacent angles.If YT is the angle bisector of ∠XYZ

what can we say aboutangles ∠XYT and ∠TYZ? ∠XYT ≅∠TYZ

So… m∠XYT =m∠TYZBy the angle addition postulate we know thatm∠XYZ = m∠XYT +m∠TYZBy substitution we have:m∠XYZ = (m∠TYZ )+m∠TYZThus,m∠XYZ = 2m∠TYZ or ½m∠XYZ = m∠TYZ

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X

T

Z

Ex #3If YT is the angle bisector of ∠XYZ and m∠XYZ = 98°what is m∠XYT?

Ex #4 If RH is the angle bisector of ∠MRD and m∠MRH = 23° what is m∠MRD?

Ex#5Find the measure between the bisector of a straight angle and one of the original rays of the straight angle.

Perpendicular lines are lines that intersect to form right angles.