1 / 21

Welcome to MM150 Unit 6

Welcome to MM150 Unit 6. Seminar. Line AB AB Ray AB AB Line segment AB AB. Plane. Any three points that do not lie on the same line determine a plane. (Since 2 points determine a line, a line and a point not on the line determine a unique plane).

alicia
Download Presentation

Welcome to MM150 Unit 6

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Welcome to MM150 Unit 6 Seminar

  2. Line ABAB • Ray ABAB • Line segment ABAB

  3. Plane • Any three points that do not lie on the same line determine a plane. (Since 2 points determine a line, a line and a point not on the line determine a unique plane). • 2. A line in a plane divides the plane into 3 parts: the line and 2 half-planes. • 3. The intersection of 2 planes is a line.

  4. 3 Definitions • Parallel planes – 2 planes that do not intersect • Parallel lines – 2 lines IN THE SAME PLANE that do not intersect • Skew lines – 2 lines NOT IN THE SAME PLANE that do not intersect.

  5. Angle D Side Vertex Side A F

  6. Angle Measures Acute Angle 0 degrees < acute < 90 degrees Right Angle 90 degrees Obtuse Angle 90 degrees < obtuse < 180 degrees Straight Angle 180 degrees

  7. More Angle Definitions 2 angles in the same plane are adjacent angles if they have a common vertex and a common side, but no common interior points. Example: [ang]BDL and [ang]LDM Non-Example: [ang]LDH and [ang]LDM 2 angles are complementary angles if the sum of their measures is 90 degrees. Example: [ang]BDL and [ang]LDM 2 angles are supplementary angles if the sum of their measures is 180 degrees. Example: [ang]BDL and [ang]LDH L M H B D

  8. If the measure of [ang]LDM is 33 degrees, find the measures of the other 2 angles. Given information: [ang]BDH is a straight angle [ang]BDM is a right angle L M H B D

  9. If [ang]ABC and [ang]CBD are complementary and [ang]ABC is 10 degrees less than [ang]CBD, find the measure of both angles. [ang]ABC + [ang]CBD = 90 Let x = [ang]CBD Then x – 10 = [ang]ABC X + (x – 10) = 90 2x – 10 = 90 2x = 100 X = 50 [ang]CBD = 50 degrees X – 10 = 40 [ang]ABC = 40 degrees D C B A

  10. Polygons

  11. Sum of Interior Angles 2 * 180 = 360 degrees 4 - 2 = 2 3 * 180 = 540 degrees 5 - 2 = 3 6 - 2 = 4 4 * 180 = 720 degrees

  12. The sum of the measures of the interior angles of a n-sided polygon is • (n - 2)*180 degrees What is the sum of the measures of the interior angles of a nonagon? n = 9 (9-2) * 180 = 7 * 180 = 1260 degrees

  13. EVERYONE: How many sides does a polygon have if thesum of the interior angles is 900 degrees? • (n - 2) * 180 = 900 • Divide both sides by 180 • n - 2 = 5 • Add 2 to both sides • n = 7 The polygon has 7 sides.

  14. Similar Figures Y B 80[deg] 80[deg] 4 4 2 2 A X Z 1 2 C 50[deg] 50[deg] 50[deg] 50[deg] [ang]A has the same measure as [ang]X [ang]B has the same measure as [ang]Y [ang]C has the same measure as [ang]Z XY = 4 = 2 AB 2 YZ = 4 = 2 BC 2 XZ = 2 = 2 AC 1

  15. Page 238 # 73 • Steve is buying a farm and needs to determine the height of a silo. Steve, who is 6 feet tall, notices that when his shadow is 9 feet long, the shadow of the silo is 105 feet long. How tall is the silo? 9 = 6 105 ? 9 * ? = 105 * 6 9 * ? = 630 ? = 70 feet The silo is 70 feet tall. ? 6 ft 9 ft 105 feet

  16. Area of a Trapezoid 3 m 2 m 4 m A = (1/2)h(b1 + b2) A = (1/2)(2)(3 + 4) A = (1/2)(2)(7) A = 1(7) A = 7 square meters

  17. Circle radius is in green diameter is in blue 2r = d Twice the radius is the diameter Circumference C = 2∏r or 2r∏ Since 2r = d C = ∏d Area A = ∏r2

  18. Prisms Pyramids

  19. Examples Page 263 #8 V = Bh V = (6 sq yd)*(6 yard) V = 36 cubic yards Page 263 #14 V = (1/3)Bh V = (1/3)(78.5 sq ft)(24 ft) V = 628 cubic feet

  20. Surface Area • Remember surface area is the sum of the areas of the surfaces of a three-dimensional figure. • Take your time and calculate the area of each side. • Look for sides that have the same area to lessen the number of calculations you have to perform.

  21. Examples Page 263 #8 Area of the 2 Bases 3 yd * 2 yd = 6 sq yd Area of 2 sides 2 yd * 6 yd = 12 sq yd Area of other 2 sides 3 yd * 6 yd = 18 sq yd Surface area 6 + 6 + 12 + 12 + 18 + 18 = 72 sq yd Page 263 #14 Surface area of a cone SA = [pi]r2 + [pi]r*sqrt[r2 + h2] SA = 3.14 * (5)2 + 3.14 * 5 * sqrt[52 + 242] SA = 3.14 * 25 + 3.14 * 5 * sqrt[25 + 576] SA = 78.5 + 15.7 sqrt[601] SA = 78.5 + SA = sq ft

More Related