SOLUTION: "If you connect the midpoints of a square, PROVE that it forms a square." I have to write a proof proving this, and I'm stuck after a certain point. I have a square "K.I.N.G." and

Question 260264: "If you connect the midpoints of a square, PROVE that it forms a square." I have to write a proof proving this, and I'm stuck after a certain point. I have a square "K.I.N.G." and its midpoints "A.B.C.D.". I have the sides of KING congruent and angles as right angles. I got the sides of ABCD congruent by the pythagorean theorum (of the small triangles in the corners of the KING square). What is the next step in proving it is a square? How do you get the angles of ABCD right angles?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
"If you connect the midpoints of a square, PROVE that it forms a square." I have to write a proof proving this, and I'm stuck after a certain point. I have a square "K.I.N.G." and its midpoints "A.B.C.D.". I have the sides of KING congruent and angles as right angles. I got the sides of ABCD congruent by the pythagorean theorum (of the small triangles in the corners of the KING square). What is the next step in proving it is a square? How do you get the angles of ABCD right angles?
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Look at one of the corner triangles.
It has a right angle and it is isosceles.
So its base angles are 45 degrees.
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This is true of each of the corner triangles.
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The side KI has two of these 45 degree angles + an angle of the inner square.
The angle of the inner square must be 90 degrees.
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And that same argument is true for side IN,NG, and GK
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Cheers,
Stan H.
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