topic: name: measuring segments · pdf filethe ruler postulate ... the segment addition...
TRANSCRIPT
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