# What do all these triangles have in common? a) 19610800081.jpg b) 19610800082.jpg c)

What do all these triangles have in common?
a)
b)
c)

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Momp1989
Step 1
As we can see all the three triangles in the image have their angles same as other
i.e. all the triangles have $$\displaystyle{45}^{{\circ}},\ {45}^{{\circ}},\ {90}^{{\circ}}$$ angles
this is also called isosceles right triangle
Step 2
A $$\displaystyle{45}^{{\circ}},{45}^{{\circ}},\ {90}^{{\circ}}$$ triangle is a special type of isosceles right triangle where the two legs are congruent to one another and the non-right angles are both equal to $$\displaystyle{45}^{{\circ}}$$ degrees. Many times, we can use the Pythagorean theorem to find the missing legs or hypotenuse of $$\displaystyle{45}^{{\circ}},\ {45}^{{\circ}},\ {90}^{{\circ}}$$ triangles. The ratio of the sides to the hypotenuse is always $$\displaystyle{1}:{1}:\sqrt{{{2}}}$$