LOP @ Ð
MNQ as corresponding angles of congruent triangles are congruent.
Another interesting property of an isosceles trapezoid is that the diagonals are equal in length.
Figure 3.10 shows an isosceles trapezoid where
LN & MO are the diagonals. It can be easily proved that seg.
LN = seg. MO. In figure 3.10 consider D
LON & D MNO.
seg. LO = seg. MN by definition of isosceles trapezoid.
Ð LON @
Ð MNO base angles are equal.
seg. ON + seg. NO same side.
D LON @
D MNO by SAS postulate
\ seg. LN
@ seg. MO as corresponding sides of congruent triangles are
The segment joining the midpoints of two sides of a triangle is parallel to the third side and half as long as the third side. Recall that the median of a trapezoid is parallel to both the bases and is half the sum of their lengths.
In figure 3.11 D ABC
can be considered to be like a trapezoid where one base is BC and
the other is point A. PQ, which is a median, is therefore parallel
to BC and is half its length.