1. Welcome to MM150 Unit 6 Seminar

2. Line AB A B AB Ray AB A B AB Line segment AB A B AB

3. Symbols Union Combining together Intersection What is shared or in common 3

4. Example: A B C AB ∩ BC BA U AD D.

5. Angle A D F Vertex Side

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 B D H L M 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: BDL and LDM Non-Example: LDH and LDM 2 angles are complementary angles if the sum of their measures is 90 degrees. Example: BDL and LDM 2 angles are supplementary angles if the sum of their measures is 180 degrees. Example: BDL and LDH

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

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

10. Parallel Lines and a Transversal The following have equal measure: Alternate Interior Angles are inside the parallel lines, and on opposite sides of the transversal. (Also, 4 and 5) Corresponding Angles are the ones at the same location at each intersection. (Also, 2 and 6; 3 and 7; 4 and 8) Alternate Exterior Angles are outside the parallel lines, and on opposite sides of the transversal. (Also, 1 and 8) Vertical Angles are opposite from each other. Like 1 and 4. Or 2 and 3. Or 5 and 8. Or 6 and 7. 10

11. Given the measure of <1 is 41 degrees, find the measure of the other angles. 11

12. Similar Figures Two figures that have the same shape are said to be similar. When two figures are similar, the ratios of the lengths of their corresponding sides are equal.similar We can use these ratios to find missing measurements. 12

13. 13 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? 6 ft 9 ft 105 feet 9 = 6 105 x 9x = 105 * 6 9x = 630 x = 70 feet The silo is 70 feet tall. Image from: http://www.abcteach.com/documents/clip-art-buildings-library-color-26143

14. Some Formulas From Text 14

15. 15 Some More Formulas From Text

16. Find the perimeter and area. P = 2b + 2w = 2(24) + 2(14) = 48 + 28 = 76 cm A = bh = (24)(10) = 240 sq.cm. 24cm 14cm 10cm

17. Composite Figures Shaded Area= Area Rectangle – Area Two Circles = lw - 2( Π r ) = (24)(14) – 2 (3.14*6 ) = 336 – 226.08 = 109.92 sq. in. 24 in Below is a rectangle with length 24 inches and width 14 inches. Two inscribed circles, of equal size, have been removed from the rectangle. Find the area of the blue shaded region. 14 in Approach: Find the area of the entire rectangle. Then, find the area of the circles. Subtract the area of the circles from the area of the rectangle. 2 2

18. Volume of a sphere with diameter 25 meters.

19. 19 Volume of a Cone Page 263 #14 V = (1/3)Bh B represents the area of the base. So, we need to find the area of the circular base. 3.14(5 ) = 3.14 (25)=78.5 sq. ft. V = (1/3)(78.5)(24) V = 628 cubic feet 2