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Geometry, etc. Review

Geometry, etc. Review. By Mrs. Heck. Most of these questions are geometry that is VERY VERY important for you to know. I slipped in a few other types that you will see on State Test! Refresh your knowledge!!!!! Have Fun --Mrs.Heck.

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Geometry, etc. Review

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  1. Geometry, etc. Review By Mrs. Heck

  2. Most of these questions are geometry that is VERY VERY important for you to know. I slipped in a few other types that you will see on State Test! Refresh your knowledge!!!!! Have Fun --Mrs.Heck

  3. An angle whose measure is between 90 and 180 degrees is called an ___________ angle. • Obtuse c) Acute • Right d) Straight

  4. Pick the algebraic expression for 5 less than the quotient of 9 and 2. • 5 - 9 x 2 c) 5 – 9/2 • 9(2-5) d) 9 / 2 -5

  5. The complement of 30° angle has a measure of _______.

  6. Find the measure of the angle. 128°

  7. A triangle with three acute angles and 3 congruent sides would be an _________ Triangle. • Scalene c) right • Isosceles d) equilateral

  8. What triangle has 3 acute angles and 2 congruent sides? • Scalene c) equilateral • Isosceles d) obtuse

  9. Simplify (45)(45) • 165 c) 425 • 410 d) 1610

  10. A circle’s perimeter is its __________? • Circumference c) Diameter • Radius

  11. Two angles are complementary if the sum of their measures is _______.

  12. Two angles are supplementary if the sum of their measures is ___________.

  13. Name the platonic solid • Cube c) Octahedron • Tetrahedron d) Dodecahedron • e) Icosahedron

  14. The distance across a circle is twice the length of its radius. That distance is the circle’s ___________. • radius c) diameter • Chord d) circumference

  15. The supplement of a 65° angle has a measure of _________.

  16. The  Tetrahedron Figure 1 Each side of the tetrahedron is in green. We will refer to the side or edge of the tetrahedron as ‘ts.’ The tetrahedron has 6 sides, 4 faces and 4 vertices. In Figure 1 the base is marked out in gray: the triangle BCD. Each of the faces is an equilateral triangle. From   The Equilateral Triangle  we know that: Area BCD = . Now we need to get the height of the tetrahedron, AH. Figure 2 From  The Equilateral Triangle  we know that: BH = . Now that we have BH, we can find  AH, the height of the tetrahedron. We will call that  h. = . = 1/3 * area BCD * h = What is the surface area of the tetrahedron?  It is just the sum of the areas of its 4 faces. We know from above that the area of a face is .The total surface area of the tetrahedron = .We have found the volume of the tetrahedron in relation to it's side. Since all 4 vertices of the tetrahedron will fit inside a sphere, what is the relationship of the side of the tetrahedron to the radius of the enclosing sphere It's easier to see the radius of the enclosing sphere if we place the tetrahedron inside a cube: Figure 3 The 4 vertices of the tetrahedron are H,F,C,A. The 4 faces of the tetrahedron in this picture are: CFH,CFA,HFA, and at the back, HCA. (The vertex D is a part of the cube, not the tetrahedron).The vertices of the cube all touch the surface of the sphere. The diameter of the sphere is the diagonal of the cube FD. In this analysis and the ones following, we will assume that all of our polyhedra are enclosed within a sphere of radius = 1. That way we will be able to accurately assess the relationship between all of the 5 regular solids. The radius of this sphere is OF = OD = 1. How does the side of the tetrahedron relate to the radius of the sphere? The side of the tetrahedron is the diagonal of the cube, as can be seen in Figure’s 3 and 4. Figure 4 FC is the side of the tetrahedron, DC is the side of the cube, FD is the diagonal of the cube and the diameter of the sphere enclosing the cube and the tetrahedron.By the Pythagorean Theorem, . , DC = 1. . FD = 2 * OF, so . Therefore, . So we write • Simplify 24 • 8 c) 6 • 16 d) 64 Figure 6 BAC and BDC are 2 intersecting faces of the tetrahedron. E is at the midpoint of BC. AE and DE are lines that go through the middle of each face and hit E. The dihedral angle is AED. The triangle EPD is right. PED = 1/2 AED by construction. AD is the side of the tetrahedron s, so PD = ½ * tsED, the height of the tetrahedron face = . sin( PED) = PD/ED = . PED = arcsin ( ) = 35.26438968 AED = 2 * PED, Dihedral angle = 70.52877936

  17. Rays, segments, or lines that form right angles are _________ • Congruent c) perpendicular • Parallel d) intersecting

  18. Find volume of the rectangular prism. 5m 8m 4m

  19. Find the volume of the cylinder. (πr2h) 4cm 8cm

  20. A _______ is a collection of points in a straight path that extends in two directions without end. • Ray b) Line • c) Line Segment d) Plane

  21. How many degrees does a right angle have?

  22. Find the measure of the angle that is supplementary to the angle having the measure of 67°.

  23. √37 is between which two consecutive whole numbers? • 3 and 7 c) 3 and 4 • 6 and 7 d) 36 and 38

  24. Find the missing angle. x 45°

  25. What is the area of the circle? (πr2) 5cm

  26. How many degrees does a straight line have?

  27. A supplementary angle to 30 degrees would be _______ degrees. Pictures downloaded from http://www.digitalmediafx.com/Shrek/shrekgallery.html http://news.bbc.co.uk/cbbcnews/hi/newsid_6630000/newsid_6632100/6632119.stm http://www.shrek.com/main.html

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