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# Maths Question (Proving sides of a square) watch

1. Hello

Recently my class did an exam paper, and a question in the back stumped me. It was a question about a square inside an isosceles triangle, and the question only gave the information that the side of the triangle was 6cm (shortest sides). The question asked to prove that the sides of the square are 2 root 2 (as shown in the diagram). I have done a mock up diagram below. I wasn't sure on what to do for this question.

2. (Original post by MersennePrime)
Hello

Recently my class did an exam paper, and a question in the back stumped me. It was a question about a square inside an isosceles triangle, and the question only gave the information that the side of the triangle was 6cm (shortest sides). The question asked to prove that the sides of the square are 2 root 2 (as shown in the diagram). I have done a mock up diagram below. I wasn't sure on what to do for this question.

Think about the hypotenuse of the triangle
3. (Original post by TeeEm)
Think about the hypotenuse of the triangle
I imagine that the hypotenuse is 3x the side of the square (36 + 36 = 72 which is 6 root 2 / 3 = 2 root 2) but why / how is the side of the hypotenuse 3x the size of the side of the square?
4. just do what TeeEm says really!
5. (Original post by MersennePrime)
I imagine that the hypotenuse is 3x the side of the square (36 + 36 = 72 which is 6 root 2 / 3 = 2 root 2) but why / how is the side of the hypotenuse 3x the size of the side of the square?
find the length of the hypotenuse
then let the side of the square be y
then mark any other length in the diagram which is y (6 in total)
6. (Original post by TeeEm)
find the length of the hypotenusethen let the side of the square be ythen mark any other length in the diagram which is y (6 in total)

Apologies for my (very) bad diagrams. Is this right?
7. (Original post by MersennePrime)
Hello

Recently my class did an exam paper, and a question in the back stumped me. It was a question about a square inside an isosceles triangle, and the question only gave the information that the side of the triangle was 6cm (shortest sides). The question asked to prove that the sides of the square are 2 root 2 (as shown in the diagram). I have done a mock up diagram below. I wasn't sure on what to do for this question.

Spoiler:
Show
angle at top left is 45 degrees thus other angle in the smaller top triangle must be 45 degrees and is isosceles so the side of that square and the little side of the big triangle at the top are the same.

(Original post by TeeEm)
find the length of the hypotenuse
then let the side of the square be y
then mark any other length in the diagram which is y (6 in total)
^^ i went on your website and your C2 papers killed me they were so difficult xD
8. (Original post by MersennePrime)

Apologies for my (very) bad diagrams. Is this right?
yup

you can simple divide 6 root 2 to become 2 root 2
9. (Original post by MersennePrime)

Apologies for my (very) bad diagrams. Is this right?
almost

the hypotenuse is root72
10. (Original post by TeeEm)
almost

the hypotenuse is root72
Yes. That's what I meant, my mistake. But I'm not sure why or how the triangles are all the same. I understand what thefatone said about the angles being the same, but same angles don't prove congruency, so how do I know each side is identical to the next?
11. (Original post by MersennePrime)
Yes. That's what I meant, my mistake. But I'm not sure why or how the triangles are all the same. I understand what thefatone said about the angles being the same, but same angles don't prove congruency, so how do I know each side is identical to the next?
you have triangles with angles 45, 45, 90
12. (Original post by MersennePrime)
Yes. That's what I meant, my mistake. But I'm not sure why or how the triangles are all the same. I understand what thefatone said about the angles being the same, but same angles don't prove congruency, so how do I know each side is identical to the next?
but they do, if you know 3 angles of a triangle it doesn't matter how big or small the triangles are they're congruent.

where congruent means the triangles are identical when superimposed?

think about it draw any triangle with the angles 45, 45 and 90 they're all congruent because the angles are the same.

Edit: i dug myself a big hole, ignore what i said up there

the small triangle on the top and bottom right both have angles of 45,45 and 90. Also the 2 sides which meet at the 90 degrees are the same, it just so happens that the 2 triangles are the same

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