Question

FG/BG=KG/CG , measure of ABG is 130 , measure of ADJ is 20

find

measure of CFD is 30

measure of GKF is 70

measure of GFK is 30

measure of G is 80

measure of GKJ is 110

Is this correct ?

Answer 1

Can you do it one angle at a time, in some logical sequence?

Answer 2

I found all the measures of the angles I just want to know if its correct. Theres no sequence they asked to find all the measures of the above listed angles

Answer 3

Right, and if you just copied the answers out of a book, there would not necessarily be a logical order to the discovery. Where did you get those values? They cannot be correct in this environment unless it is known from whence they came.

Answer 4

I conclude them based on the information they gave which is FG/BG=KG/CG , measure of ABG is 130 , measure of ADJ is 20

Answer 5

They asked to find the measures of angles CFD, GKF, GFK, G and GKJ to which I did based on the information and picture given

Answer 6

Non-responsive.

You may wish to rethink \(m\angle CFD\)

Answer 7

angle FCD is 130 and ADJ is 20 then CFD has to be 30 is that not correct

Answer 8

In order for \(m\angle FCD\) to be 130º, \(\triangle BGC\) would have to be isosceles. That information is not given. Do we know it's isosceles?

Answer 9

Would FG/BG=KG/CG do it?

Answer 10

No good. Notice how the ratios refer only to pieces of \(\triangle BGC\) and to pieces of the smaller triangle \(\triangle FGK\). It's trying to tell you, with the included \(\angle G\), that these two triangles are similar.

Answer 11

I see, so what should CFD be then I really dont know

Answer 12

This is why I wanted to see a logical sequence.

First, ignoring the Similar Triangles, I think the most obvious
information is \(m\angle GBC = 50º\). Do you see that this is so?

Answer 13

Yes 180-130=50

Answer 14

Perfect. The next logical piece might be \(m\angle BKD = 110º\). Where did I get that?

Answer 15

180-(50+20)

Answer 16

Excellent. You spotted \(\triangle BKD\)!

Okay, next we can have \(\angle GKF = 70º\). Why?

Answer 17

180-110

Answer 18

Linear Pairs strike again! Unfortunately, this is the end of our little angle trail. Try as we might, there appears to be no more information to be gleaned from ignoring the similar triangles.

Something that helps me see it is to redraw the triangles I'm trying to compare. It's hard to see them all jumbled up, together. Draw \(\triangle BGC\) and \(\triangle FGK\) somewhere off by themselves. This will un-confuse us.

Answer 19

The next thing is to remember the various definition of things for Triangles.

SideSideSide produces congruent triangles. We won't need that.
SideAngleSide produces congruent triangles. We won't need that.
AngleSideSide produces the "Ambiguous Case". We need to be careful with that.
AngleAngleAngle produces Similar Triangles. Too bad we have only angle G.

CPCTC - The old corresponding parts of congruent triangles are congruent.
CPSTAP - This is the Similar Triangle version. Corresponding Parts of Similar Triangles are Proportional!!!!

Oh, I like the word "Proportional", since that is EXACTLY the kind of information we need.

We are told that to pair of corresponding parts of two triangles are proportional. We also know the angle between them is congruent, since angle G is the sme in both triangles.

Where does that lead us?

Answer 20

Wow sorry I just looked at the problem again and it says assume the triangle an isosceles triangle .... That makes things a lot easier

Answer 21

Well, without that assumption, the similar triangles give us \(\angle GFK = 50º\;and\;\angle GCB = 70º\) and this makes us just about done.

Good luck with that.

Answer 22

Wouldnt GCB be 50 because its congruent with GBC

Answer 23

If it's isosceles. Yes.

Answer 24

You said 70 got me confused there for a second