Question

The measure of EB is _[blank A]_ units by the _[blank B]_. Thus, BC must measure _[blank C]_ units.

Match each blank with the number or theorem that correctly fills in that blank.

Blank A:

Blank B:

Blank C:

Possible Answers:
40
80
100
60
Converse of triangle proportionality theorem

Triangle Proportinality theorem

Answer 1

(A)60

(B)Triangle Proportionality theorem

(C)100

Explanation:

Triangle Proportionality theorem

If a line parallel to one side of a triangle intersects the other two sides of the triangle, then the line divides these two sides proportionally.

By this theorem, In the given triangle ABC,

`(|AD|)/(|DB|)=(|CE|)/(|EB|) \\(32)/(48)=(40)/(|EB|) \\|EB| X 32 =40 X 48\\|EB|=40 X 48 / 32\\|EB|=60 \:Units`

|BC|=|EB|+|CE|

=60+40

|BC|=100 Units

Therefore:

The measure of EB is 60 units by the Triangle Proportionality theorem. Thus, BC must measure 100 units.