Theorem: A line parallel to one side of a triangle divides the other two proportionately.

In the figure below, segment DE is parallel to segment BC and segment EF is parallel to AB:

The figure shows triangle ABC with segments DE and EF. Point D is on side AB, point E is on side AC and point F is on side BC.

Which statement can be proved true using the given theorem? (6 points)

Select one:

a. Segment BF = 16

b. Segment BD = 20 Incorrect

c. Segment BD = 15

d. Segment BF = 32

C

Step-by-step explanation:

Since DE is parallel to BC then the 2 sides are divided into the same proportion, that is

= , substitute values

= = ( cross- multiply )

6BD = 90 ( divide both sides by 6 )

BD = 15 → C

option a, c,d are correct.

step-by-step explanation:

from the given figure, it is given that z is equidistant from the sides of the triangle rst, then from triangle tzb and triangle szb, we have

tz=sz(given)

bz=zb(common)

therefore, by rhs rule,δtzb ≅δszb

by cpctc, sz≅tz

also, from δctz and δasz,

tz=sz(given)

∠tcz=∠saz(90°)

by rhs rule, δctz ≅ δasz, therefore by cpctc, ∠ctz≅∠asz

also,from δasz and δzsb,

zs=sz(common)

∠zbs=∠saz=90°

by rhs rule, δasz ≅δzsb, therefore, by cpctc, ∠asz≅∠zsb

hence, option a, c,d are correct.

step-by-step explanation: