Download 1.4 Notes

Geometry
Unit 1B
Section 1.4
Angles and Their Measures
The figure formed by two rays with a common
An *angle is ________________________________________________
A
_____________________________________________________
endpoint
The rays are the __________
Sides of the angle and their common endpoint is
the ____________
vertex of the angle
B
1
C
The same angle can be named in different ways:
3 points-with the middle point being the vertex
1) ___________________________________________________________________________________
 CBA
 ABC
___________
or ____________
A small number inside the angle near the vertex
2) ___________________________________________________________________________________
1
___________
Just the vertex when there is only 1 angle with that vertex
B
3) ___________________________________________________________________________________
________________________________
_________
protractor
Angles are measured using a __________________.
A common unit used for measuring angles is the
A
degrees We write ________
m
___________.
to represent the measure of  A .
Their measures are equal
Two angles are congruent if ________________________________________________.
Tick marks are used to indicate congruent angles in a figure.
Angles are classified according to their measure.
Less than 90 degrees
An *acute angle is an angle whose measure is _____________________________.
Exactly 90 degrees
A *right angle is an angle whose measure is _____________________________.
To indicate a right angle in a figure, place a small square at the vertex.
To form a right angles
*Perpendicular lines are two lines that intersect _____________________________________.
AB CD
To indicate that AB is perpendicu lar to CD , we write _______________
Greater than 90 degrees
An *obtuse angle is an angle whose measure is _____________________________.
Exactly 180 degrees
A *straight angle is an angle whose measure is _____________________________.
The Angle Addition Postulate is similar to the Segment Addition Postulate.
Postulate 4: Angle Addition Postulate: The measure of the angle PQR is equal to the measure
of angle SQR plus the measure of angle PQS
If S is in the interior of  PQR , then _____________________________
A ray which divides the angle into two congruent angles.
An *angle bisector is ___________________________________________________________________
_____________________________________
A
D
ABC Entire angle = 8x + 16
96
2𝑥 − 8 + 2𝑥 − 8 + 96 = 8𝑥 + 16
2𝑥 − 8
E
2𝑥 − 8
B
C
4𝑥 + 80 = 8𝑥 + 16
64 = 4𝑥
X=16
The measurement of angle DBC
2𝑥 − 8
2 ∗ 16 − 8 = 24
24 ∗ 2 = 48