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Presentation Details: Slides: 15 Duration: 00:05:16 Filename: C:\Users\jpage\Documents\NCVPS Learning Objects\Math 3\Math 3 Angles and Parallel Lines Navigation to PPT W\Angles and Parallel Lines.ppt Presenter Details: Angles and Parallel Lines Published by Articulate® Presenter www.articulate.com Slide 1 Angles and Parallel Lines Angles and Parallel Lines Duration: 00:00:10 Advance mode: Auto Slide 2 Parallel Lines Parallel Lines Duration: 00:00:47 Advance mode: Auto • Lines that are coplanar and NEVER intersect. – Remember that COPLANAR means on the same plane These are two parallel lines. They will keep extending in both directions and never intersect. B A AE, DH, CG, BF would all be parallel to each other. AB, DC, HG, EF would all be parallel to each other. C D E H Published by Articulate® Presenter AD, BC, FG, EH would all be parallel to each other. F G Notes: In this module, you will learn about two different types of lines, parallel and skew. You will also be introduced to four new angle pairs and their properties. Notes: Parallel lines are lines that are coplanar and that never intersect. If you recall, coplanar lines were lines that were on the same plane. Never intersect means that the lines will never cross. In the first picture, the two lines will keep extending indefinitely and will never cross, so they will be defined as parallel lines. In the three dimensional box, there are three sets of parallel lines. AB, DC, GH, and EF (the lines in green) are all parallel lines. AD, BC, EH, and GF (the lines in blue) would all be parallel lines. AE, BF, CG, and DH (the lines in red) are all parallel lines. www.articulate.com Slide 3 Notes: Parallel Lines There are two symbols to know for parallel lines. One is for written instructions. That is the first symbol. Two small lines that are parallel written between two lines means parallel. The other symbol is for pictures. When there are arrows on the lines, it means the lines are parallel. If there is one arrow on the line, it would be parallel to any other line with one arrow. If there are two arrows on a line, it would be parallel to a line with two arrows, etc. Duration: 00:00:31 Advance mode: Auto Slide 4 Duration: 00:00:26 Advance mode: Auto Notes: Skew Lines Skew Lines • Lines that are NON-coplanar that NEVER intersect. – Remember that NON-coplanar means not on the same plane. B A DC and GF would be skew lines. C D AE and HG would be skew lines. E F H Slide 5 You try…. Duration: 00:00:06 Advance mode: By user G You try…. 1. 2. 3. 4. 5. 6. Name a line parallel to XY. Name a line parallel to WS. Name a line parallel to UT. Name a line skew to YZ. Name a line skew to XR. Name a line skew to UR. Notes: You try these examples. See the last slide in the presentation to check your answers. W X Z Y R U Published by Articulate® Presenter Another type of line that will never intersect is skew lines. Skew lines are NON-coplanar lines that will never intersect. Since they are noncoplanar, that means they are not on the same plane. AE and HG (lines in blue) are an example of skew lines. DC and GF (lines in red) are an example of skew lines. Can you come up with any other examples? S T www.articulate.com Slide 6 Transversal Transversal Duration: 00:00:13 Advance mode: Auto • A line that intersects at least two other lines in two distinct points. transversal Slide 7 Alternate Interior Angles Duration: 00:00:18 Advance mode: Auto Alternate Interior Angles • A pair of angles that are on opposite sides of the transversal but inside the two lines. transversal 1 3 5 2 4 A transversal is a line that intersects two or more other lines in distinct points. When a transversals intersects lines it creates some new angle pairs. Proceed in the presentation to learn these new angle pairs. Notes: Alternate interior angles are a pair of angles that are on opposite sides of the transversal, and are inside the two lines. Opposite makes them alternate, while being inside makes then interior. When the two lines are parallel, alternate interior angles are always CONGRUENT. 6 3 and 6 would be alternate interior angles. 8 7 Notes: 4 and 5 would be alternate interior angles. • When the two lines are parallel, then alternate interior angles are CONGRUENT. Slide 8 Alternate Exterior Angles Duration: 00:00:24 Advance mode: Auto Alternate Exterior Angles • A pair of angles that are on opposite sides of the transversal but outside the two lines. transversal 1 3 5 7 2 4 6 8 1 and 8 would be alternate exterior angles. Notes: Alternate exterior angles are a pair of angles that are on opposite sides of the transversal and are outside the two lines. Like alternate interior angles, they are on opposite sides of the transversals, but unlike alternate interior angles, alternate exterior angles are outside the two lines. When the two lines are parallel, alternate exterior angles are always CONGRUENT. 2 and 7 would be alternate exterior angles. • When the two lines are parallel, then alternate exterior angles are CONGRUENT. Published by Articulate® Presenter www.articulate.com Slide 9 Corresponding Angles Duration: 00:00:18 Advance mode: Auto Corresponding Angles • A pair of angles that sit in the same corner of the transversal but on a different line. transversal 1 and 5 would be corresponding angles. 1 3 5 2 and 6 would be corresponding angles. 2 4 6 8 7 3 and 7 would be corresponding angles. Notes: Corresponding angles are a pair of angles that are on the same corner of the transversal but are on different lines. Corresponding angle pairs also have one angle that is interior and one angle that is exterior. When the two lines are parallel, corresponding angles are always CONGRUENT. 4 and 8 would be corresponding angles. • When the two lines are parallel, then corresponding angles are CONGRUENT. Slide 10 Consecutive Interior Angles Duration: 00:00:22 Advance mode: Auto Consecutive Interior Angles • A pair of angles that are inside the lines and on the same side of the transversal. • Also called same-side interior angles. transversal 1 3 5 7 2 4 6 3 and 5 would be cosecutive angles. 8 Notes: Consecutive interior angles are a pair of angles that are on the same side of the transversal and are inside the two lines, making then interior. Because they are on the same side of the transversal, consecutive interior angles may also be called same-side interior angles. When the two lines are parallel, consecutive interior angles are SUPPLEMENTARY. 4 and 6 would be consecutive angles. • When the two lines are parallel, then consecutive angles are SUPPLEMENTARY. Slide 11 Examples Duration: 00:01:15 Advance mode: By user Examples Find the measure of angle 1. 1. 2. 56 1 1 91 3. 4. 134 1 85 1 Published by Articulate® Presenter Notes: 1. These are corresponding angles because they sit in the same corner of the transversals (upper right side) but are on different lines. When lines are parallel, corresponding angles are congruent, so angle 1 = 56°. 2. These are consecutive interior angles because they sit on the same side of the transversal (the bottom side) and they are inside the lines. When lines are parallel, consecutive angles are supplementary, which means they add to equal 180°, so angle 1 = 89°. www.articulate.com 3. These are alternate interior angles because they sit on opposite sides of the transversal (one on the top, one on the bottom) and they are inside the lines. When lines are parallel, alternate interior angles are congruent, so angle 1 = 85°. 4. These are alternate exterior angles because they sit on opposite sides of the transversal (one on the left, one on the right) and they are on the outside of the lines. When lines are parallel, alternate exterior angles are congruent, so angle 1 = 134°. Slide 12 You try…. Find the measure of angle 1. You try…. Find the measure of angle 1. 1. 2. Duration: 00:00:05 Advance mode: By user Notes: You try these examples. See the last slide in the presentation to check your answers. 81 75 1 1 3. 4. 155 101 1 1 Slide 13 You try… Duration: 00:00:05 Advance mode: By user You try… Find x. 1. 2. Notes: You try these examples. See the last slide in the presentation to check your answers. Find the measure of the angle in bold. 3. Bold angle is bottom angle. 4. Bold angle is top angle. Published by Articulate® Presenter www.articulate.com Slide 14 Solutions Duration: 00:00:05 Advance mode: By user Slide 15 Answers to You Try slides… Duration: 00:00:09 Advance mode: By user Published by Articulate® Presenter 1. 87 = 7x + 10 - 10 - 10 77 = 7x 7 7 x = 11 2. 75 = 8x + 11 - 11 - 11 64 = 8x 8 8 x=8 3. 22x + 4 + 35x + 5 = 180 57x + 9 = 180 -9 -9 57x = 171 57 57 x=3 35x + 5 = 35(3) + 5 = 110 4. 14x + 4 + 6x – 4 = 180 20x = 180 20 20 x=9 These are the solutions to the problems on the previous you try slide. 14x + 4 = 14(9) + 4 = 130 Answers to You Try slides… Parallel/Skew Lines 1. WZ, ST, RU 2. ZT, YU, XR 3. RS, XW, YZ 4. XR, WS, RU, ST 5. YZ, UT, WZ, ST 6. YZ, WX, ZT, WS Notes: Angles 1. 105 2. 81 3. 155 4. 101 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 Knowledge activity. Find x. 1. 11 2. 8 Find the angle in bold. 3. 110 4. 130 www.articulate.com