# Thread: Triangle in a square

1. ## Triangle in a square

Attached (not to scale)

The equilateral triangle inside the square. Find angle DEC.

I've had a long look at it and can't find the answer. I've found a lot of other angles but not the one I need!

Any help appreciated

Attached (not to scale)

The equilateral triangle inside the square. Find angle DEC.

I've had a long look at it and can't find the answer. I've found a lot of other angles but not the one I need!

Any help appreciated

I've attached a figure with some angles filled in. Can you find your missing angle from this? Remember that the base angles of an isosceles triangle are congruent.

3. Thanks for you reply, but I can't see the diagram to clearly.

Thanks for you reply, but I can't see the diagram to clearly.
Click on the diagram and it will enlarge.

5. Originally Posted by masters
Click on the diagram and it will enlarge.
I tried that, bit it doesn't get any bigger. However, from what I can tell, you seem to be showing that the side of teh square is the same as the side of the equaliater triangle.....omg, of course it is!! Sorry, actually had the eureka moment as I was typing this.

Got it now.

Thanks!!!

I tried that, bit it doesn't get any bigger. However, from what I can tell, you seem to be showing that the side of teh square is the same as the side of the equaliater triangle.....omg, of course it is!! Sorry, actually had the eureka moment as I was typing this.

Got it now.

Thanks!!!
Great! Now, I've included a better image for you to see.

7. Originally Posted by masters
Great! Now, I've included a better image for you to see.
i wanna ask how do u know that AD=AE & BC=BE_______to get thatDAe is isoscles....thnx

8. Originally Posted by lebanon
i wanna ask how do u know that AD=AE & BC=BE_______to get thatDAe is isoscles....thnx
Hello lebanon,

We are told that the triangle is equilateral (all sides are congruent). One side of the equilateral triangle is on the square. So this means the sides of the square are congruent to the sides of the triangle.

Look at the markings I have made on the sides of the triangle and square, indicating which triangles formed are isosceles. It should be pretty apparent if you know anything about isosceles triangles.