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Introduction to Angles Definitions Vertex: Common endpoint of the two rays that make an angle. A Point B is the vertex of โ ๐จ๐ฉ๐ช B C Sides: The two rays that make up the angle. A side ๐ฉ๐จ and ๐ฉ๐ช are sometimes B called sides. side C Angle and Points ๏ฌ An Angle is a figure formed by two rays with a common endpoint, called the vertex. ray vertex ๏ฌ ray Angles can have points in the interior, in the exterior or on the angle. A E D B C Points A, B and C are on the angle. D is in the interior and E is in the exterior. B is the vertex. Lesson 1-4: Angles 3 Naming an angle: (1) Using 3 points (2) Using 1 point (3) Using a number โ next slide Using 3 points: vertex must be the middle letter This angle can be named as ๏ABC or ๏CBA Using 1 point: using only vertex letter * Use this method is permitted when the vertex point is the vertex of one and only one angle. Since B is the vertex of only this angle, this can also be called ๏B . B Lesson 1-4: Angles A C 4 Naming an Angle - continued Using a number: A number (without a degree symbol) may be used as the label or name of the angle. This A number is placed in the interior of the angle near its vertex. The angle to the left can be named B 2 C as ๏2 . * The โ1 letterโ name is unacceptable when โฆ more than one angle has the same vertex point. In this case, use the three letter name or a number if it is present. Lesson 1-4: Angles 5 Definitions Measure of an angle: Smallest amount of rotation about the vertex from one ray to the other. Use a curved line to indicate the angle. A B ๐๐° C Degrees: The unit of measure for angles. Indicates the amount of rotation. โ ๐จ๐ฉ๐ช = ๐๐° Example ๏ฌ K is the vertex of more than one angle. Therefore, there is NO ๏K in this diagram. There is ๏LKM , ๏PKM , and ๏LKP There is also ๏2 and ๏3 but there is no ๏5!!! L M 2 K 3 Lesson 1-4: Angles P 7 4 Types of Angles Acute Angle: an angle whose measure is less than 90๏ฐ. Right Angle: an angle whose measure is exactly 90 ๏ฐ. Obtuse Angle: an angle whose measure is between 90๏ ๏ฐ and 180๏ฐ. Straight Angle: an angle that is exactly 180 ๏ฐ. Lesson 1-4: Angles 8 Definitions Congruent Angles: Angles that have the same degree measure. Used a curved line above an equal sign to indicate congruence. A X โ B C Y Z โ ๐จ๐ฉ๐ช โ โ ๐ฟ๐๐ Said: โAngle ABC is congruent to angle XYZ.โ Practice Name all the angles in this figure. P โ ๐ท๐ฟ๐ฎ โ ๐ฎ๐ฟ๐ด โ ๐ท๐ฟ๐ด โ ๐ฟ๐ด๐ฎ โ ๐ฟ๐ฎ๐จ โ ๐ฟ๐ฎ๐ด โ ๐ด๐ฎ๐จ X M G A Measuring, calculating and drawing angles... 0011 0010 1010 1101 0001 0100 1011 1 2 4 0011 0010 1010 1101 0001 0100 1011 A protractor 1 2 4 Here is a standard protractor like you use in the classroom. When we use a protractor, we need to line it up correctly. 0011 0010 1010 1101 0001 0100 1011 1 2 4 You need to make sure the protractor is lined up correctly. Is this ready to measure the angle? Were you right......................it wasnโt 0011 0010 1010 1101 0001 0100 1011 1 2 4 Look for the upside down โTโ in the middle of the straight line on your protractor. This needs to be exactly on the vertex of your angle. We need to remember..... 0011 0010 1010 1101 0001 0100 1011 It doesnโt matter which way round the angle is, you ALWAYS need to line the upside down โTโ to the vertex of the angle. 1 2 4 Now you are ready. 0011 0010 1010 1101 0001 0100 1011 1 2 4 Read from the 0°, and follow the inner set of numbers. Once you reach 30° you need to be careful!!! 0011 0010 1010 1101 0001 0100 1011 1 2 4 You then need to look at the 1° markings on the outer set of numbers. What does it measure? 0011 0010 1010 1101 0001 0100 1011 1 This angle measures 35°. 2 4