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2. m AE = m AB

MTH-5109 Pretest

Identify the theorem that applies to the items below.

1.

THEOREM NUMBER

__________________________________

24

THEOREM NUMBER

__________________________________

4

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:

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

- Determine if the statements below are true or false and if true state the theorem that applies given that:
- m OF = m OG

- mAOE = m ACE ______________
- m BD = m BC ______________
- m CE = m ED ______________

True Th. 14

False

True Th. 5

Given: true state the theorem that applies given that:

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

m BC = 2 m true state the theorem that applies given that: AED – 2 mABD

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

Proj from Bracket true state the theorem that applies given that:

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

C true state the theorem that applies given that:

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

C true state the theorem that applies given that:

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

B true state the theorem that applies given that:

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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