2007-09-28 04:15:21 · 3 answers · asked by *purple world* 4 in Science & Mathematics ➔ Mathematics
Draw a trapezoid.
The legs are congruent since it is isoceles.
The bottom base is congruent after you draw the diagonals.
The base angles are congruent.
By SAS, the diagonals are congruent.
QED
2007-09-28 04:19:04 · answer #1 · answered by Anonymous · 0⤊ 0⤋
Because the trapezoid is isosceles, the nonparallel sides have equal length. Of course, the bottom side is equal to itself (reflexive property). Finally, since the trapezoid is isosceles the base angles are equal.
Therefore, If you draw the diagonals you can describe a situation where you have two triangles that are congruent by SAS (side, angle, side). From this, the two diagonals have equal length.
2007-09-28 04:20:21 · answer #2 · answered by Mathsorcerer 7 · 0⤊ 0⤋
you take the two triangles, ABD and ACD. they have a common side which is AD, two equal sides: AB and CD .. since it's isosceles. And two equal angles, the angles in point A and point D. Therefore the triangles are equivalent and the 3rd sides have to be equal to each other. So that's why the diagonals are equal.
2007-09-28 04:28:12 · answer #3 · answered by lachlaan2004 3 · 0⤊ 0⤋