Objectives: 1) Find the lengths of segments 2) Find the measures of angles 1-4 Measuring Segments & Angles M11.B.2 M11.C.1 2.5.11.B 2.3.11.B.

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Presentation transcript:

Objectives: 1) Find the lengths of segments 2) Find the measures of angles 1-4 Measuring Segments & Angles M11.B.2 M11.C B B

Here is a Ruler… What is the distance between points C and D? | | | | | | | | | | C D

Postulate 1-5: Ruler Postulate The points of a line can be put into one-to-one correspondence with the real numbers so that the distance between any two points is the absolute value of the difference of the corresponding numbers. BA.. The length of AB = |a-b| **Think back to our ruler…|2-5| = 3 and |5-2| = 3 25

Vocabulary Congruent Segments - Two segments with the same length. **congruent symbol (=) Ex) If AB = CD, then AB = CD ~ ~ D B DC A C AB 2 cm

Example 1: Comparing Segment Lengths Find which two of the segments XY, ZY and ZW are congruent. WZY X 6

Postulate 1-6 : Segment Addition Postulate If three points A, B, and C are collinear and B is between A and C, then AB + BC = AC BCA.

Example 2: Segment Addition Postulate If XY = 10, YZ = 6 and ZW = 8, what is XW? X Y Z W If MP = 37 and NP = 25, what is MN? M N P

Example 3: Using the Segment Addition Postulate If AB = 25, find the value of x. Then find AN and NB. NBA. 2x - 6x + 7

Vocabulary Midpoint – a point that divides a segment into two congruent segments. A midpoint “bisects” the segment. BCA.

Example 4: Using Midpoint M is the midpoint of NO and NM = 12. Find MO and NO. DRAW A PICTURE!!

Example 5: Finding Lengths M is the midpoint of RT. Find RM, MT and RT. MTR. 5x + 98x - 36

Vocabulary Angle (/)- formed by two rays with the same endpoint. The rays are the sides of the angle. Endpoint is the vertex. Label angles by their sides or vertex... Q B T

Example 6: Naming Angles Name in 4 Ways.. Z X Y 3

Classifying Angles Acute Angle0<x<90 Right Anglex= 90 Obtuse Angle 90<x<180 Straight Angle x = 180 **To indicate the size or degree measure of an angle, write a lowercase “m” in front of the angle symbol. Example:

Example 7: Measuring & Classifying Angles Classify the Angles 12

Vocabulary Congruent Angles – Angles with the same measure. Ex) m<1 = m<2, then <1 = <2 ~

Postulate 1-8: Angle Addition Postulate If point B is in the interior of <AOC, then m<AOB + m<BOC = m<AOC If <AOC is a straight angle, then m<AOB + m<BOC = 180 C B C B O O A A

Example 8: Using the Angle Addition Postulate Suppose that m<1 = 42 and the m<ABC = 88. Find m< C B A

Example 9: Angle Addition Postulate If m < DEG = 145, find m < GEF. G D E F