In figure,points A and B are on the same side of a line m,AD perpendicular m and BE perpendicular m and meet m at D and E respectively. If C is the mid point of AB,prove thatCD =CE
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AB//CL//BE. as AD CL and BE are perpendicular made from the same line.
So, by intercept theorem
AD//CL//BE. and ACB and DLE are transverse lines so as AC=CB then DL= LE
Join CD and CE
IN DLC and CLE
DL=LE
CL IS COMMON
angle DLC = angle CLE
therefore triangle DLC is congruent to triangle CLE .
CD= CE ( cpct)
So, by intercept theorem
AD//CL//BE. and ACB and DLE are transverse lines so as AC=CB then DL= LE
Join CD and CE
IN DLC and CLE
DL=LE
CL IS COMMON
angle DLC = angle CLE
therefore triangle DLC is congruent to triangle CLE .
CD= CE ( cpct)
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