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Presentation Details: Slides: 17 Duration: 00:05:26 Filename: C:\Users\jpage\Documents\NCVPS Learning Objects\Geometry Angles Navigation to PPT W\GeometryAngles\Mod 2 Les 1.pptx Presenter Details: Module 2 Lesson 1 Angles Published by Articulate® Presenter www.articulate.com Slide 1 Notes: Module 2 Lesson 1 Angles Module 2 Lesson 1 Angles Duration: 00:00:09 Advance mode: Auto Slide 2 Ray Duration: 00:00:32 Advance mode: Auto In this module, you will be introduced to angles and constructions. In this lesson, you will be introduced to what makes an angle and what some special angle pairs are. Ray Notes: • A portion of a line that starts at one point and extends indefinitely in one direction C A B • Name: must be named using the endpoint FIRST, then another point on the ray • Symbol: a ray drawn above the name AB A ray is a portion of a line that starts at one point but extends indefinitely in one direction. So a ray has a starting point, but no ending point. To name a ray, you MUST use the starting point as the start of the name. The second point can be any point that is on the ray. The ray in the figure would then be ray AB. Ray BA would be incorrect because the ray does not start at B and ray AC would be incorrect because C is in the other direction of the ray. NOT BA or AC Slide 3 Opposite Rays Duration: 00:00:23 Advance mode: Auto Opposite Rays Notes: • Two rays that have the same starting point but extend in opposite directions. Y X XZ and XY are opposite rays Z Opposite rays are two rays that have the same starting point but extend in opposite directions. Opposite rays always form a line and a straight angle. In the diagram, ray XZ and ray XY are opposite rays. They share a starting point of X but ray XY extends to the left and ray XZ extends to the right. • Form a line and straight angle. Published by Articulate® Presenter www.articulate.com Slide 4 Angles Duration: 00:00:24 Advance mode: Auto Notes: Angles • Made of two rays that have a common endpoint • The rays are considered the sides of the angle. • The common endpoint is considered the vertex of the angle. A Sides: BA, BC Vertex: point B An angle is a geometric figure that is formed by two rays. These rays will have a common endpoint, that endpoint will be known as the vertex of the angle. The vertex gives the location of the angle. The two rays will be the sides of the angle. The angle pictured has a vertex at point B and the sides of the angle will be ray BA and ray BC. B C Slide 5 Naming an Angle Duration: 00:00:33 Advance mode: Auto Naming an Angle Notes: • An angle can be named in three different ways 1. Using the vertex (can only have one angle with that vertex) B 2. Using three different points (vertex must be in the middle) ABC or CBA 3. Using a number B 1 A 1 C Slide 6 Types of Angles Duration: 00:00:35 Advance mode: Auto Types of Angles 1. Acute Angle – an angle that measures between 0 and 90 . 2. Right Angle – an angle that measures exactly 90 . 3. Obtuse Angle – an angle that measures between 90 and 180 . 4. Straight Angle – an angle that measures exactly 180 . Published by Articulate® Presenter Angles can be named in three different ways. Way one is to use the vertex point. The angle would be called angle B. This way can only be used when there is only one angle with that vertex. Way two is to use three different points. The vertex must be the middle point in the name. The angle would be called angle ABC or angle CBA. Both have point B in the middle. Way three is to use a number given in the diagram. The angle would be called angle 1. Notes: There are four different types of angles. The smallest is an acute angle. An acute angle measures more than 0 degrees but less than 90 degrees. The second type is a right angle. A right angle measure exactly 90 degrees. Right angles will be marked with a box at the vertex of the angle. The third type is an obtuse angle. An obtuse angle measures more than 90 degrees but less than 180 degrees. The fourth type is a straight angle. A straight angle measures exactly 180 degrees. www.articulate.com Slide 7 You try... You try…Identify the type of angle shown. 1. 2. Duration: 00:00:06 Advance mode: By user 3. Duration: 00:00:21 Advance mode: Auto You try these examples. See the last slide in the presentation to check your answers. 4. Slide 8 Adjacent Angles Notes: Adjacent Angles • Adjacent angles are two angles that share a vertex and have one side in common. DGE is adjacent to EGF E D Vertex: point G Notes: Adjacent angles are a set of two angles that share a vertex and have a common side. Adjacent angles also have no interior points in common. Point G would be the vertex to both angles and the common side would be ray GE. Angle DGE would be adjacent to angle EGF. Common side: GE F G Slide 9 Vertical Angles Vertical Angles Duration: 00:00:32 Advance mode: Auto • Vertical angles are two angles created by interesting lines. Share a vertex and have no interior points in common. Vertex: point M HML is vertical to JMK HMJ is vertical to LMK J H M K L Vertical angles are always CONGRUENT. Published by Articulate® Presenter Notes: Vertical angles are a set of angles that are created by two intersecting lines. Vertical angles share a vertex but nothing else. With each set of intersecting lines, there will be two different sets of vertical angles. Angle HML would be vertical to angle JMK. Angle HMJ would be vertical to angle LMK. One thing to remember about vertical angles is that they will always be congruent. Remember that congruent means that they have the same measure. www.articulate.com Slide 10 Linear Pair Linear Pair Duration: 00:00:33 Advance mode: Auto Notes: • A linear pair is two angles that share a vertex, have a common side, and their non common sides are opposite rays. Vertex: point N NP and NM are opposite rays. MNO and ONP are a linear pair. O M P N Linear pairs are two angles that share a vertex and a common side. Their non common sides form opposite rays. Remember that opposite rays are two rays that have the same starting point and extend in opposite directions. Point N would be the vertex of both angles. Ray NP and ray NM would be opposite rays. Angle MNO and angle ONP would be a linear pair. Linear pairs will always have a sum of 180°. Linear pairs always have a sum of 180 . Slide 11 Complementary Angles Duration: 00:00:16 Advance mode: Auto Complementary Angles Notes: Complementary angles are a pair of angles that when added together will equal 90°. Complementary angles may be adjacent, making a right angle, like in picture 1, or complementary angles many be nonadjacent, like in picture 2. • Complementary angles are two angles that have a sum of 90 . Picture 2 Picture 1 67 50 23 40 Complementary Angles can be adjacent or nonadjacent. Slide 12 Supplementary Angles Duration: 00:00:16 Advance mode: Auto Notes: Supplementary Angles • Supplementary angles are two angles that have a sum of 180 . Picture 1 Picture 2 Supplementary angles are a pair of angles that when added together will equal 180°. Supplementary angles may be adjacent, making a linear pair, like in picture 1, or supplementary angles may be nonadjacent, like in picture 2. 58 115 65 122 Supplementary angles can be adjacent or nonadjacent. Published by Articulate® Presenter www.articulate.com Slide 13 Perpendicular Angles Perpendicular Angles Duration: 00:00:19 Advance mode: Auto • Perpendicular angles are angles that are formed by perpendicular lines. • Each angle will always have a measure of 90 . Notes: Perpendicular angles are angles that are formed by perpendicular lines. These angles are always right angles, therefore they will always have a measure of 90°. An important fact to know is that if there is one right angle pictured, then their will be a total of four right angles in the figure. If there is one right angle, then there are a total of four right angles. Slide 14 You try... Duration: 00:00:06 Advance mode: By user You try…Give the most specific angle pair for angles 1 and 2. Notes: 1. You try these examples. See the last slide in the presentation to check your answers. 2. 2 1 1 3. 2 4. 2 1 1 2 1 5. 2 Slide 15 You try... You try….Find the measure of angle 1. 1. 2. Notes: k nk Duration: 00:00:06 Advance mode: By user 1 n 1 124 3. 4. 36 You try these examples. See the last slide in the presentation to check your answers. 62 1 1 Published by Articulate® Presenter www.articulate.com Slide 16 You try... Duration: 00:00:06 Advance mode: By user You try…. Find the value of x. 1. ab Notes: You try these examples. See the last slide in the presentation to check your answers. 2. 5x + 2 7x - 1 6x Find the value of the angle indicated. 3. 4. Find m NQP. Find mCBD. O B A N 6x + 10 4x + 10 7x - 11 Q M C 9x + 5 D P Slide 17 Answers to You Try Slides Duration: 00:00:10 Advance mode: By user Answers to You Try Slides Identify the type of angle shown 1. straight 2. obtuse 3. right 4. acute Give the most specific angle pair for angles 1 and 2. 1. complementary 2. adjacent 3. linear pair or supplementary 4. vertical 5. perpendicular angles Find the measure of angle 1. 1. 124° 2. 90° Find the value of x. 1. 13 3. 144° Notes: Here are the answers to each of the you try slides. I hope you did well. After you have completed this presentation, proceed with the Check Your Understanding activity. 4. 28° 2. 8 Find the value of the angle indicated. 3. 38° 4. 104° Published by Articulate® Presenter www.articulate.com