Below is the Isosceles triangle ABC (AC = AB):
In its interior, a line ED is drawn parallel to CB.
Is the triangle AED also an isosceles triangle?
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Below is the Isosceles triangle ABC (AC = AB):
In its interior, a line ED is drawn parallel to CB.
Is the triangle AED also an isosceles triangle?
To demonstrate that triangle AED is isosceles, we must prove that its hypotenuses are equal or that the opposite angles to them are equal.
Given that angles ABC and ACB are equal (since they are equal opposite bisectors),
And since ED is parallel to BC, the angles ABC and ACB alternate and are equal to angles ADE and AED (alternate and equal angles between parallel lines)
Opposite angles ADE and AED are respectively sides AD and AE, and therefore are also equal (opposite equal angles, the legs of triangle AED are also equal)
Therefore, triangle ADE is isosceles.
AED isosceles
If one of two corresponding angles is a right angle, then the other angle will also be a right angle.
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