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

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x A D C B 3. Given the circle below, if m ABC = x, determine a simplified expression for m ADC. 4. Given the 2 circles, determine: A B Area 1 = 200.96 cm 2 Area 2 = 50.24 cm 2

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A B GF E D C 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 AB CF 5. Determine the perimeter of ΔBCF, ΔABF and ΔBDF.

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A B GF E D C

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

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AB C D EF 7. Which of the following statements are true? Which theorem supports your choice. Given: 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 Diameter of inner circle = Diameter of outer circle False True Th. 11 True Th. 12

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

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WALL SHELF 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. Bracket 2 = Span Proj from Bracket 36 2 = 60 Proj from Bracket Proj from Bracket = 1296 ÷ 60 Proj from Bracket = 21.6 Th. 23 Proj from Bracket Proj from Shelf = 60 - 21.6 = 38.4 Shelf 2 = Span Proj from Shelf Shelf 2 = 60 38.4 Shelf 2 = 2304 Shelf = 48 cm Th. 23

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10. Determine A H M B CD Th. 19 Th. 25 Th. 23

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11.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? h w z y x A F D B E H G C O 12.In the diagram to the right find m EHF given: m EC = 64 ; m FD =54 ; m EAC = 20 ; m CB = 120 STATEMENTSJUSTIFICATIONS True Th. 23 False True Th. 25 Theorem 17

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

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13.In the diagram to the right find. 14.In the diagram to the right: Segment BM is a median and measures 5 cm. Segment BH is an altitude and measures 4 cm.. B A H C M B A 21.7 H C 50 30° Th. 20 Th. 24 Th. 19 Th. 23

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