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MTH-5109 Pretest

2. m AE = m AB. MTH-5109 Pretest. Identify the theorem that applies to the items below. 1. THEOREM NUMBER __________________________________. 24. THEOREM NUMBER __________________________________. 4. C. x. D. B. A. B. A. Area 1 = 200.96 cm 2. Area 2 = 50.24 cm 2.

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MTH-5109 Pretest

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  1. 2. m AE = m AB MTH-5109 Pretest Identify the theorem that applies to the items below. 1. THEOREM NUMBER __________________________________ 24 THEOREM NUMBER __________________________________ 4

  2. C x D B A B A Area1 = 200.96 cm2 Area2 = 50.24 cm2 3. Given the circle below, if m ABC = x, determine a simplified expression for m ADC. 4. Given the 2 circles, determine:

  3. AB CF B A F G C E D 5. Determine the perimeter of ΔBCF, ΔABF and ΔBDF. BE is a perpendicular bisector to CF AB is a tangent to the circle at B AF is a tangent to the circle at F

  4. B A F G C E D

  5. Determine if the statements below are true or false and if true state the theorem that applies given that: • m OF = m OG • mAOE = m ACE ______________ • m BD = m BC ______________ • m CE = m ED ______________ True Th. 14 False True Th. 5

  6. Given: D Diameter of inner circle = A B E F Diameter of outer circle C 7. Which of the following statements are true? Which theorem supports your choice. a) Circumference of the outer circle is 9 times the circumference of the inner circle. False b) Dark shaded area = 9 times the white area False c) Circumference of the inner circle is one-third of the circumference of the outer circle. True Th. 11 True Th. 12 d) Dark shaded area = 8 times the white area

  7. m BC = 2 mAED – 2 mABD A B E D C STATEMENTS JUSTIFICATIONS 8. Refer to the diagram to the right to prove the statement: Use theorems to justify your work where it is appropriate. Theorem 16 Theorem 15 Substitution

  8. Proj from Bracket WALL SHELF Bracket S P A N 9. Calculate the width of a shelf that is affixed to a wall as shown in the accompanying diagram. The shelf is attached to the wall using a bracket that makes contact with the wall over a distance of 36 cm. The shelf is strengthened by 60 cm span running from the outside edge of the shelf to the bottom of the bracket. An altitude that attaches the span to the intersection of the shelf and bracket fortifies it even more. Do not use Pythagorean Theorem. Bracket2 = Span • Proj from Bracket 362 = 60 • Proj from Bracket Proj from Bracket = 1296 ÷ 60 Proj from Bracket = 21.6 Th. 23 Proj from Shelf = 60 - 21.6 = 38.4 Shelf2 = Span • Proj from Shelf Shelf2 = 60 • 38.4 Shelf2 = 2304 Shelf = 48 cm Th. 23

  9. Th. 19 Th. 25 Th. 23 Th. 23 A M H B C D • Determine

  10. C E G y z H O F h B D w x A • In the right triangle, h is the altitude from the hypotenuse. • Determine which statements below are true and if they are what theorem can be used to justify this? True Th. 23 False True Th. 25 • In the diagram to the right find m EHF given: m EC = 64; m FD =54; m EAC = 20; m CB = 120 STATEMENTS JUSTIFICATIONS Theorem 17

  11. C E mFB = mDF + mBD mFB = 54 + 24 = 78º G H O F B D mEF = 360º - (mFB + mBC + mCE) A mEF = 360º - (78 + 120 + 64) = 360º - 262º = 98º STATEMENTS JUSTIFICATIONS Theorem 16 Theorem 15

  12. B 21.7 30° A C H 50 B A C H M • In the diagram to the right find . Th. 20 Th. 24 • In the diagram to the right: • Segment BM is a median and measures 5 cm. • Segment BH is an altitude and measures 4 cm. . Th. 19 Th. 23

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