Question

Proof: @jhonyy9

Answer 1

Can i do this proof all at once? I know how to state c and d not a or b

Answer 2

Skype?

Answer 3

Um, sorry i dont have just explain it here

Answer 4

the big enigma, that I can see is, BC, is BC perpendicular to EA?, and that's not really certain

Answer 5

@Agl202

Answer 6

BAD and EAC are indeed similar, by ASA for one

Answer 7

or not even that, but just AA will do anyway

Answer 8

and since both of those guys are similar indeed, so are their proportions, meaning AD/AC = BA/EA

Answer 9

and you can do a cross-multiplication on those proportions, and you'll end up with BA * AC = EA * AD

Answer 10

now, the isosceles bit... that one is where the issue lies.... and for that, dunno if BC is really perpendicular to EA, is not clear there

Answer 11

Well, thats my problem how do i prove that

Answer 12

Do you need a formal 2-column proof?

Answer 13

If a segment bisects an angle of a triangle, then the two segments of the divided side are proportional to the two sides.

Answer 14

The triangle proportionality theorem (also called the side splitter theorem)
If a segment is parallel to one side of a triangle, then it divides the other two sides into proportional segments.

Answer 15

Yes i need a two column proof can you start from proving its an issocles

Answer 16

So, letters b,c,d is one proof and letter a is a separate proof i guess

Answer 17

In this problem, both of those situations are present.

Answer 18

ok

Answer 19

I figured out the isosceles part.

Answer 20

looks like hes got you ^^

Answer 21

True

Answer 22

Start the proof.
Write the givens, and the reason is given.

Answer 23

k

Answer 24

Using the parallel lines, and the triangle proportionality theorem, you can write this proportion:

\(\dfrac{AB}{BE} = \dfrac{AD}{DC}\) Reason: theorem mentioned above.

Answer 25

Using the bisected angle, write this proportion:

\(\dfrac{AB}{AD} = \dfrac{BC}{DC}\) Reason: Triangle angle bisector theorem.

Answer 26

There is a property of proportions that is like this:

If \(\dfrac{a}{b} = \dfrac{c}{d}\), then \(\dfrac{a}{c} = \dfrac{b}{d} \).

Answer 27

Use the first proportion and the property of proportions above to write:

\(\dfrac{AB}{AD} = \dfrac{BE}{BC} \)

Answer 28

So everything in one proof?

Answer 29

fyi, for 7a.
you can use alternate interior angles (of transversal across 2 parallel lines)
to claim < DBC= < BCE
also, exterior angle of a triangle equals the sum of the two opposite angles
i.e. <ABC= <AEC + <BCE

Answer 30

Okay, so thats where the parallel lines comes in.

Answer 31

Yes.
The second proportion above had AB/AD = BC/DC
We also have AB/AD = BE/DC
By substitution we now have:
\(\dfrac{BC}{DC} = \dfrac{BE}{DC} \)
Multiplying both sides by DC, you get BC = BE
The triangle is isosceles.

Answer 32

Wow, i just need help writing it all down in steps and knowing what comes first

Answer 33

so here is how to do it using angles