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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 __________________________________. THEOREM NUMBER __________________________________. 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 __________________________________ THEOREM NUMBER __________________________________

  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 m AB = 12 cm m BC = 10 cm m CG = 2.8 cm m DG = 3.7 cm

  4. Determine if the statements below are true or false and if true state the theorem that applies given that: • m OF = m OG; m CAB = m BD. Given: D A B E F C • mAOE = m ACE ______________ • m BD = m BC ______________ • m CE = m ED ______________ 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. b) Dark shaded area = 9 times the white area c) Circumference of the inner circle is one-third of the circumference of the outer circle. d) Dark shaded area = 8 times the white area

  5. m BC = 2 mABD – 2 mAED 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.

  6. A M H B C D 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. • Determine m CM = 6.5 cm m AH = 3.2 cm m CD = 12 cm CM is a median to AD.

  7. 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? • In the diagram to the right find m EHF given: m EC = 64; m FD =54; m EAC = 20; m CB = 120 STATEMENTS JUSTIFICATIONS

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

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