Clickers Bellwork Solve for x 3x+5+2x-4=36.

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1.4 Measure and Classify Angles

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Presentation transcript:

Clickers Bellwork Solve for x 3x+5+2x-4=36

Bellwork Solution Solve for x

Bellwork Solution Solve for x

Bellwork Solution Solve for x

Measure and Classify Angles Section 1.4

The Concept Today we’re going to discuss the different kinds of angles We’re also going to talk about adding and bisecting angles

Definition Angle Object that is created by the connection of two rays at the same endpoints Consists of two sides and a vertex Named by three points (of which one is the vertex) or just by the vertex if it is not shared with another angle Object that is created by the connection of two rays at the same endpoints Consists of two sides and a vertex Named by three points (of which one is the vertex) B Angle 1.4 A C Indicates angle Axis of symmetry Vertex

Congruence Similar to our look at line segments, we have to be aware of the difference in use of the congruence and equals signs

Protractor Postulate The measure of an angle (denoted m) is equal to the absolute value of the difference between the real numbers for the two rays as they cross a protractor In other words, if you measure an angle with a protractor we can be reasonably certain that it’s correct…

Classification There are four kinds of angles Acute Right Obtuse Measuring less than 90 degrees Right Measuring 90 degrees Obtuse Measuring larger than 90 degrees and less than 180 Straight Measuring 180 degrees A C B A C B A C A B C

On your own What kind of angle is shown below?

On your own What kind of angle is shown below?

On your own What kind of angle is shown below?

Angle Addition Postulate If P is in the interior of ∠RST, then the measure of ∠RST is equal to the sum of the measures of ∠RSP and ∠PST. R P S T

Example R P 35 S 23 T 58o

On your own What is the measure of angle ABD, if the measure of angle ABC is 102o? B 35o C A D

Application Find if is 72 degrees R P 3x+6 S 2x-9 T

Congruency Two angles that have the same measure are considered congruent Example 4

Homework 1.4 2-38 even, 51-58 (don’t measure, just classify)

Bisector angles Similar to bisectors of lines, a bisector of an angle is a ray that shares the end point of a given angle that splits the measure of the angle in half R P S T

Application Find if is 32o and SP is a bisector R P S T

Most Important Points Definition of angles Classification of angles Angle addition postulate Congruent Angles Bisector angles