Transcript Slide 1

MTH-5109 Pretest
Identify the theorem that applies to the items below.
1.
m BD 
m AB  m BC
m AC
B
THEOREM NUMBER
__________________________________
A
D
2. m AE = m AB
THEOREM NUMBER
__________________________________
B
A
F
E
C
C
O
D
3. Given the circle below, if m ABC = x, determine a
simplified expression for m ADC.
C
x
D
A
4. Given the 2 circles,
determine: r
1
r2
, r1, and r2
m AB  12cm
Area1 = 200.96 cm2
Area2 = 50.24 cm2
A
B
B
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
B
A
AF is a tangent to the circle
at F
AB
CF
m AB = 12 cm
m BC = 10 cm
m CG = 2.8 cm
m DG = 3.7 cm
F
G
C
E
D
6. 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.
A
B
F
a) m AOE = m ACE ______________
C
O
b) m BD = m BC ______________
G
c) m CE = m ED ______________
D
E
7. Which of the following
statements are true? Which
theorem supports your choice.
Given: m AB  m CD  m EF
D
A
B
C
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 onethird of the circumference of the outer
circle.
d) Dark shaded area = 8 times the white area
E
F
8. Refer to the diagram to the right to prove the
statement:
m BC = 2 mABD – 2 mAED
Use theorems to justify your work
where it is appropriate.
A
D
B
E
C
STATEMENTS
JUSTIFICATIONS
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.
WALL
SHELF
10.
Determine
m AB and m BC .
m CM = 6.5 cm
m AH = 3.2 cm
m CD = 12 cm
CM is a median to AD.
A
M
H
B
C
D
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?
1.
y w z

z
y
____________________
2.
h2  z w
____________________
3. w  x 2  y 2  z
y
z
h
________________
w
x
12. In the diagram to the right find m EHF
given:
m EC = 64; m FD =54; m EAC = 20; m CB = 120
STATEMENTS
C
E
JUSTIFICATIONS
G
H
O
F
B
D
A
13. In the diagram to the right find m AB .
B
21.7
30°
A
50
C
H
14. In the diagram to the right:
Segment BM is a median and measures 5 cm.
B
Segment BH is an altitude and measures 4 cm.
.
m AB  8cm
Find m CH
A
M
H
C