Consider a trapezoid figure 3.8 where the legs are equal in length.
This is called as an isosceles trapezoid.
In figure 3.8 seg.LO = seg.MN. Therefore, LMNO is an isosceles trapezoid. In such a trapezoid the base angles are equal. This can be proven by drawing two altitudes from L & M on the seg.ON.
Figure 3.9 shows LP & MQ as two altitudes of
LOP & D MNQ. Both are right
triangles such that their hypotenuse has the same length ( LMNO
is an isosceles trapezoid ).
Also seg. LP = seg MQ as the perpendicular distance between two paralles lines is always the same.
\ By HS postulate D
LOP @ D