Isoceles Triangle: Find Measure of Angle DFG

[Dragondude]

Homework Statement

triangle dfg and triangle fgh are isoceles. measure of angle fdh=28. dg=fg=fh. Find measure of angle dfg.

Homework Equations

The Attempt at a Solution

 

[HallsofIvy]

I don't see any way of determining that. We can take angle dfg to be any number less than 28, make angle gfh 28 minus that angle, and have the situation you describe.

 

[Dragondude]

Could you use SSS or something like that ?

 

[Dragondude]

HallsofIvy are you still there?

 

[Dragondude]

I took another look. I would only use the isoceles triangle theorem...right?

 

[Gear300]

I took another look at the problem. Could you not use the Isocelses triangle theorem? Then use the angle sum theorem?

yup...I'd say you could...though...HallsofIvy is more understanding with mathematics, so you might want to wait for an answer from him for a better perspective.

 

[Dragondude]

Thanks Gear300. I will still take your advice on waiting for HallsofIvy to answer. But thanks very MUCH.

 

[HallsofIvy]

I took another look at the problem. Could you not use the Isocelses triangle theorem? Then use the angle sum theorem?

What do you mean by "the isosceles triangle theorem"? That the base angles are equal? That would help you knew one of angles in one of the two isosceles triangles- but you don't. Are you assuming that the two triangles are congruent? You didn't say that.

Without that, as I said before, you could construct two triangles, having vertex angles that sum to 28 degrees, that would satisfy the conditions here. The vertex angle dfg could be anything from 0 to 28.

 

[Dragondude]

But the Isoceles triangle theorem says that if two sides of a triangle are congruent then the angles opposite those sides are congruent. So if you used that theorem with triangle dfg then you could say that angle dfg is 28 degrees, because angle fdh is 28 degrees. Right? Can you take a look at post #7 where I said maybe I could use only use the Isoceles triangle theorem.

 

[HallsofIvy]

fdh is not an angle in any isosceles triangle. The base angles of triangle dgf are fdg and dfg. The base angles in triangle fgh are hgf and fhg. fdh is a an angle in triangle fdh which is NOT isosceles.

 

[Dragondude]

I checked the book and it said I was right. Here is a picture of the triangle in my book.

 

[HallsofIvy]

Thanks. For some reason that wasn't at all how I visualized it! Yes, in that picture, fdh is a base angle in an isosceles triangle and is congruent to dfg.