Thread: Similar triangles

I have an equillateral triangle and require to calculate the lengths of two parallel lengths.

I have included a sketch to help identify.

BC = AB = AC
YZ AY AZ

I know;

AB = 3
AC = 3
AY = 2
AZ = 2

I require to find the ratios BC and YZ

AB = AC = BC
AZ AY YZ

3 = 3 = x
2 2 x

How do I work with this method above to isolate BC and YZ

Originally Posted by David Green

I have an equillateral triangle and require to calculate the lengths of two parallel lengths.
How do I work with this method above to isolate BC and YZ

Because .

Originally Posted by Plato

Because .

The problem there is that you have given two unknowns on the LHS, where both cannot be solved at the same time?

I know the answers, but I don't know how to perform the algebra to solve the lengths of the sides?

Originally Posted by David Green

The problem there is that you have given two unknowns on the LHS, where both cannot be solved at the same time? I know the answers, but I don't know how to perform the algebra to solve the lengths of the sides?

It is an equilateral triangle:

Originally Posted by Plato

It is an equilateral triangle:

I know its an equilateral triangle, and I know each angle is 60 degrees, and I know AB = 3, BC = 3, and AC = 3, and YZ = 2

I just can't prove it mathematically

Originally Posted by David Green

I know its an equilateral triangle, and I know each angle is 60 degrees, and I know AB = 3, BC = 3, and AC = 3, and YZ = 2

I just can't prove it mathematically

It's a given, you don't need to prove it. Unless you've mistyped the question

Originally Posted by david green

i know its an equilateral triangle, and i know each angle is 60 degrees, and i know ab = 3, bc = 3, and ac = 3, and yz = 2
i just can't prove it mathematically

Help!

Thanks for info.