SOLUTION: Miss Allan has a piece of paper in the shape of a right-angled triangle
𝐴𝐵𝐶 (with the right-angle at 𝐴). She folds vertex 𝐵 over onto the midpoint
of 𝐴𝐶, the
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-> SOLUTION: Miss Allan has a piece of paper in the shape of a right-angled triangle
𝐴𝐵𝐶 (with the right-angle at 𝐴). She folds vertex 𝐵 over onto the midpoint
of 𝐴𝐶, the
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Question 1204709: Miss Allan has a piece of paper in the shape of a right-angled triangle
𝐴𝐵𝐶 (with the right-angle at 𝐴). She folds vertex 𝐵 over onto the midpoint
of 𝐴𝐶, then flattens the paper out to give a right-angled quadrilateral.
What is the exact ratio of the area of this new quadrilateral to the area of
the original triangle? Answer by math_tutor2020(3820) (Show Source):
You can put this solution on YOUR website!
Hint:
Right triangle ABC is folded over line EF to form trapezoid AEFC.
Point B will move to point D. None of the other labeled points move.
I recommend cutting out a piece of paper to do the fold yourself.
Some more hints
AB = 2*AE
AC = 2*EF
E and F are midpoints of AB and BC respectively
area of a triangle = 0.5*base*height
area of a trapezoid = 0.5*height*(base1+base2)
Technically the formulas aren't needed because there's an intuitive approach using the diagram shown above. But it doesn't hurt to use the formulas anyway.
Edit: The student has requested another hint. Notice how, based on the folds, we have 4 small congruent triangles.
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