Question

Bernardo is converting a fraction, StartFraction a Over b EndFraction, to a percent. Both a and b are whole numbers and not equal to zero. Which expression represents the percent?
(a divided by b) divided by 100
(b divided by a) divided by 100
100 (a divided by b)
100 (b divided by a)

Answer 1

Answer:

DBC________

Fig. 3.30

... angle BAC angleBDC (c.a.c.t.)

In A ABC, ZBAC = 60° . ZBDC = 60°

ZDAC = ZADC = ZACD = 60°... sum of angles of A ADC is 180°Kk

.: AADC is an equilateral triangle.

.. AC = AD = DC ........ corollary of converse of isosceles triangle theorem

1

But AB = AD........ construction

2

1

..AB AC ........ * AD= AC

2

1 / 2Proof : /\ ABC and /\ DBC

seg AB seg DB

___________

angle ABC segment Angle DBC________

seg BC seg BC_______

.. A ABC = A DBC________

Fig. 3.30

... angle BAC angleBDC (c.a.c.t.)

In A ABC, ZBAC = 60° . ZBDC = 60°

ZDAC = ZADC = ZACD = 60°... sum of angles of A ADC is 180°

.: AADC is an equilateral triangle.

.. AC = AD = DC ........ corollary of converse of isosceles triangle theorem

1

But AB = AD........ construction

2

1

..AB AC ........ * AD= AC

2

1 / 2Theorem: If the acute angles of a right angled triangle have measures 30° and 60°, then

the length of the side opposite to 30° angle is half the length of the hypotenuse,

(Fill in the blanks and complete the proof.)

Given : In A ABC

ZB = 90°, ZC = 30°, ZA= 60°

60

To prove : AB

-

AC

30

B

C С

Fig. 3.29

Construction : Take a point D on the extended

seg AB such that AB = BD. Draw seg DC.

Proof : /\ ABC and /\ DBC

seg AB seg DB

___________

angle ABC segment Angle DBC________

seg BC seg BC_______

.. A ABC = A DBC________

Fig. 3.30

... angle BAC angleBDC (c.a.c.t.)

In A ABC, ZBAC = 60° . ZBDC = 60°

ZDAC =

angle ABC segment Angle DBC________

seg BC seg BC_______

.. A ABC = A DBC________

Fig. 3.30