Warm-up 1)What is the difference between drawing and constructing a geometric figure? 2)Draw an angle with measure of 55°

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Presentation transcript:

Warm-up 1)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 Measure Degree Protractor Acute Angle Right angle Obtuse angle Straight Angle Congruent Angles Straight Edge Ruler Compass Draw Sketch Construct Postulates 4.1 Protractor Postulate 4.2 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 ∠ DBC By substitution: (105°) = (35°) + m ∠ DBC - 35° -35° - 35° -35° 70 ° = m ∠ DBC 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 about angles ∠XYT and ∠TYZ? ∠XYT ≅∠TYZ So… m m m m∠XYT =m∠TYZ By the angle addition postulate we know that m∠XYZ = m∠XYT +m∠TYZ By substitution we have: m∠XYZ = (m∠TYZ )+m∠TYZ Thus, m∠XYZ = 2m∠TYZ or ½m∠XYZ = m∠TYZ Y X T Z

Ex #3 If 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#5 Find 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.