Objectives: Measure angles with a protractor Identify and use the angle addition postulate Warm-Up: Find the indicated value. AC = 20; AB = _____ A BC.

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Presentation transcript:

Objectives: Measure angles with a protractor Identify and use the angle addition postulate Warm-Up: Find the indicated value. AC = 20; AB = _____ A BC x-4 2x+3

Vocabulary: Degree: The most common unit of angle measure. (this is the unit of measure that results when a half circle is divided into 180 equal parts)

Vocabulary: Protractor: A geometric ruler that is a half-circle with coordinates from 0 o to 180 o.

Vocabulary: Measure of an Angles: m<AVB is |a – b| or |b – a| A B V

Vocabulary: Complementary Angles: Two angles whose measures have a sum of 90 o (each angle is called the compliment of the other) 60 ⁰ 30 ⁰ 23 ⁰ 67 ⁰

Vocabulary: Supplementary Angles: Two angles whose measures have a sum of 180 o (each angle is called the supplement of the other) 137 ⁰ 43 ⁰

Vocabulary: Linear Pair: When the endpoint of a ray falls on a line so that two angles are formed, then the angles are known as a linear pair. 1 2 Linear Pair Property: Linear Pair Property: If two angles form a linear pair they are supplementary.

Vocabulary: Angle Congruence Postulate: If two angles have the same measure then they are congruent. If two angles are congruent then they have the same measure.

Types of Angles: Right Angle: Obtuse Angle: Acute Angle: An angle whose measure is 90 ⁰ An angle whose measure is less than 90 ⁰ An angle whose measure is greater than 90 ⁰ and less than 180 ⁰

Vocabulary: Angle Addition Postulate: If point S is in the interior of < PQR the m < PQS + m < SQR = m < PQR Q P S R

Example 1: Measure of an Angles: m<AVB is |a – b| or |b – a| A B C D m < BAC = ______ m < CAD = ______ m < BAD = ______

Example 2: Identify the Congruent Angles. AB D C

Name all the complementary and supplementary angle pairs. Complementary angles: ____ & _____ B A C Supplementary angles: ____ & _____ 60 o 30 o 120 o Example 3:

Collins Writing Type 1: In creating a protractor, does the size of the half-circle make a difference?

Find the missing angle measures. B E Example 4: M T m < BTE = 40 ⁰, m < ETM = 60 ⁰, m < BTM = ______ m < BTE = 112 ⁰, m < ETM = ______, m < BTM = 168 ⁰ m < BTE = ______, m < ETM = 47 ⁰, m < BTM = 92 ⁰

m < XTY = 42 ⁰ < WTX and < XTZ form a linear pair. Find the following: m < XTY = 42 ⁰ and < WTX and < XTZ form a linear pair. Find the following: W X Example 5: Z T m < YTZ = ______ m < WTX = ______ m < WTY = ______ m < XTZ = ______ Y

E F Example 6: D S m < DSF = (45 + x) ⁰, find the value of x and then give each indicated angle measure. m < DSF : m < DSE : m < ESF : (5x+4) ⁰ (4x+1) ⁰

E F Example 7: D A m < BAD = 82 ⁰ & m < CAE = 64 ⁰ find: m < 1 : m < 2 : m < 3 : m < 4 : m < BAF: B C 4

Homework: pages (21 problems) #’s 13-19, 27-34, 36-38, 42-44