1.4Measure and Classify Angles
description
Transcript of 1.4Measure and Classify Angles
![Page 1: 1.4Measure and Classify Angles](https://reader036.fdocuments.in/reader036/viewer/2022062422/56813c03550346895da56468/html5/thumbnails/1.jpg)
1.4 Measure and Classify Angles
You will name, measure and classify angles.
![Page 2: 1.4Measure and Classify Angles](https://reader036.fdocuments.in/reader036/viewer/2022062422/56813c03550346895da56468/html5/thumbnails/2.jpg)
Classifying Angles• Acute angle: between 0 and 90
• Right angle: exactly 90 degrees• Symbol:
• Obtuse Angle: between 90 and 180
• Straight angle: exactly 180 degrees
![Page 3: 1.4Measure and Classify Angles](https://reader036.fdocuments.in/reader036/viewer/2022062422/56813c03550346895da56468/html5/thumbnails/3.jpg)
Angles
• Naming Angles– Use 3 capital letters – Vertex in the middle– Can use one capital letter if it is the vertex and it is
obvious which angle you are referring to– Can use the number located inside the angle
• Angle Bisector– Divides the angle into 2 congruent parts
![Page 4: 1.4Measure and Classify Angles](https://reader036.fdocuments.in/reader036/viewer/2022062422/56813c03550346895da56468/html5/thumbnails/4.jpg)
Naming angles
• Name this angle three different ways
![Page 5: 1.4Measure and Classify Angles](https://reader036.fdocuments.in/reader036/viewer/2022062422/56813c03550346895da56468/html5/thumbnails/5.jpg)
Naming angles
• Name this angle three different ways
![Page 6: 1.4Measure and Classify Angles](https://reader036.fdocuments.in/reader036/viewer/2022062422/56813c03550346895da56468/html5/thumbnails/6.jpg)
Naming angles
• Name this angle four different ways
![Page 7: 1.4Measure and Classify Angles](https://reader036.fdocuments.in/reader036/viewer/2022062422/56813c03550346895da56468/html5/thumbnails/7.jpg)
Name this angle in 4 ways
![Page 8: 1.4Measure and Classify Angles](https://reader036.fdocuments.in/reader036/viewer/2022062422/56813c03550346895da56468/html5/thumbnails/8.jpg)
Congruent Angles
• Have the same angle measure
![Page 9: 1.4Measure and Classify Angles](https://reader036.fdocuments.in/reader036/viewer/2022062422/56813c03550346895da56468/html5/thumbnails/9.jpg)
Congruent Angles
• Can be marked using the same number of hash marks.
H
W
F
Q
![Page 10: 1.4Measure and Classify Angles](https://reader036.fdocuments.in/reader036/viewer/2022062422/56813c03550346895da56468/html5/thumbnails/10.jpg)
Angle Addition Postulate
• Smaller angles can be added together to form larger angles if they share a common vertex.
![Page 11: 1.4Measure and Classify Angles](https://reader036.fdocuments.in/reader036/viewer/2022062422/56813c03550346895da56468/html5/thumbnails/11.jpg)
Given that the m<LKN=145⁰, find the m<LKM and m<MKN
![Page 12: 1.4Measure and Classify Angles](https://reader036.fdocuments.in/reader036/viewer/2022062422/56813c03550346895da56468/html5/thumbnails/12.jpg)
GUIDED PRACTICE for Example 3
Find the indicated angle measures.
3. Given that <KLM is a straight angle, find x and m< NLM.
![Page 13: 1.4Measure and Classify Angles](https://reader036.fdocuments.in/reader036/viewer/2022062422/56813c03550346895da56468/html5/thumbnails/13.jpg)
GUIDED PRACTICE for Example 3
4. Given that < EFG is a right angle, find x and m< HFG.
![Page 14: 1.4Measure and Classify Angles](https://reader036.fdocuments.in/reader036/viewer/2022062422/56813c03550346895da56468/html5/thumbnails/14.jpg)
Homework
• Page 28 # 4 – 40 even
• Honors: also # 42, 44, 48, 49, 50
![Page 15: 1.4Measure and Classify Angles](https://reader036.fdocuments.in/reader036/viewer/2022062422/56813c03550346895da56468/html5/thumbnails/15.jpg)
EXAMPLE 2 Measure and classify angles
Use the diagram to find the measure of the indicated angle. Then classify the angle.
a. KHJ b. GHK c. GHJ d. GHL
SOLUTION
A protractor has an inner and an outer scale. When you measure an angle, check to see which scale to use.
![Page 16: 1.4Measure and Classify Angles](https://reader036.fdocuments.in/reader036/viewer/2022062422/56813c03550346895da56468/html5/thumbnails/16.jpg)
Angle Addition Postulate
• When two angles share a ray, a Part+ Part = Whole or Little + Little = Big
• Very similar to segment addition Postulate
![Page 17: 1.4Measure and Classify Angles](https://reader036.fdocuments.in/reader036/viewer/2022062422/56813c03550346895da56468/html5/thumbnails/17.jpg)
Congruent Angles
• Angles that have the same measure• Angle measures are equal: m<A=m<B– The measure of angle A is equal to the measure of
angle B• Angle measures are congruent: <A <B– Angle A is congruent to angle B
• When talking about measures, use equal sign. When talking about congruency, use congruent sign
![Page 18: 1.4Measure and Classify Angles](https://reader036.fdocuments.in/reader036/viewer/2022062422/56813c03550346895da56468/html5/thumbnails/18.jpg)
EXAMPLE 4 Identify congruent angles
The photograph shows some of the angles formed by the ropes in a trapeze apparatus. Identify the congruent angles. If m<DEG = 157° ,what is m<GKL?
![Page 19: 1.4Measure and Classify Angles](https://reader036.fdocuments.in/reader036/viewer/2022062422/56813c03550346895da56468/html5/thumbnails/19.jpg)
GUIDED PRACTICE for Example 4
5. Identify all pairs of congruent angles in the diagram.
Use the diagram shown.
![Page 20: 1.4Measure and Classify Angles](https://reader036.fdocuments.in/reader036/viewer/2022062422/56813c03550346895da56468/html5/thumbnails/20.jpg)
GUIDED PRACTICE for Example 4
6. In the diagram, m < PQR = 130 , m<QRS = 84, and m<TSR = 121 . Find the other angle measures in the diagram.
Use the diagram shown.
![Page 21: 1.4Measure and Classify Angles](https://reader036.fdocuments.in/reader036/viewer/2022062422/56813c03550346895da56468/html5/thumbnails/21.jpg)
Angle
• Formed by two rays that meet at an endpoint• Rays are considered sides of an angle• What is the vertex? What rays form the angle?
![Page 22: 1.4Measure and Classify Angles](https://reader036.fdocuments.in/reader036/viewer/2022062422/56813c03550346895da56468/html5/thumbnails/22.jpg)
Vertex of an Angle
• Where the sides of an angle meet.• When naming an angle, vertex goes in the
middleName the three angles in the diagram.
![Page 23: 1.4Measure and Classify Angles](https://reader036.fdocuments.in/reader036/viewer/2022062422/56813c03550346895da56468/html5/thumbnails/23.jpg)
Angle bisector
A ray that divides an angle into two angles that are congruent (equal)
In the diagram at the right, YW bisects < XYZ, and m< XYW = 18. Find m< XYZ.
![Page 24: 1.4Measure and Classify Angles](https://reader036.fdocuments.in/reader036/viewer/2022062422/56813c03550346895da56468/html5/thumbnails/24.jpg)
Protractor Postulate
• The rays of an angle can be matched one to one with real numbers from 0 to 180
• The measure of an angle is equal to the absolute value of the difference between the real number of the rays (much like the segment addition postulate)