Topic:

Measuring Segments and Angles

(Sections 1.2a and 1.3a)

Name: ____________________________________________________

Period: ________ Date: ___________________________

Primary Assignment: __________________________________________ Secondary Assignment: _________________________________________

Questions and Main Ideas Notes

The Ruler Postulate

• The numbers are called _________________ • The distance along a line is ______________ until a ______ is chosen • ______________________. If you get a negative number, take the absolute value.

Example 1: Calculate the length of each segment

A) XY = B) ZY =

The Segment Addition Postulate

Example 2: Calculate NO

Congruent vs. Equal

• ____________ segments have the same lengths.

• The word ___________ is used with numbers. PQ = RS

• The word ___________ is used with objects. 𝑃𝑄̅̅ ̅̅ 𝑅𝑆̅̅̅̅

• Use tick marks in diagrams to show segments are congruent

AB = |a – b| or |b - a| A

a

B

b

Example 3:

The map shows the route for a race. You are 365m from drink station R and 2km from drink station S. The first-aid station is located at the midpoint of the two drink stations. How far are you from the first-aid station?

Example 4: Using a midpoint

D is the midpoint of 𝐸𝐹̅̅ ̅̅ , ED = 4x + 6, and DF = 7x – 9. A) Model the situation. B) Write a Geometric equation based on your model. C) Calculate ED, DF, and EF.

Angles • An angle is a figure formed by two ________, called sides, with a common endpoint called the ________ (plural: vertices).

• There are 3 ways to name an angle: • By the vertex • By a number in the interior • With 3 points: one from each side and the

_________ in the __________ • If more than 1 angle shares a vertex you can NOT

name the angle solely by its vertex!

Example 5: Naming Angles

A) What are two other names for 2?

B) Why can’t 1 be called M?

The Protractor Postulate

• Angles describe ___________, NOT length • Angles are measured in __________ using a protractor or in __________.

Read “the measure of angle AOB is 125

degrees”

125om AOB

Classifying Angles

_____________ ______________ ______________ ______________

• Angles with the same measure are ____________ angles.

Example 6: Measuring Angles

• Use a protractor to measure each angle. • Classify each angle as acute, obtuse, right, or straight.

The Angle Addition Postulate

Examples 7 & 8 mDEG = 115°, and mDEF = 48°. Calculate m∠MNO and m∠PNO

Find mFEG.

Angle Bisector • An angle bisector is a ray that divides an angle into _____________ angles.

• 𝐽𝐾⃗⃗⃗⃗ bisects LJM; thus LJK KJM.

Example 9 𝐾𝑀 ⃗⃗⃗⃗⃗⃗ ⃗⃗ bisects JKL, mJKM = (4x + 6)°, and mMKL = (7x – 12)°. Find mJKM.

Symbol for congruent angles in diagrams

x

3x - 2

M

P N

O