Area Theorems


   
 
Theorem 3
The area of a triangle is half that of a parallelogram standing on the same base and between the same parallels.
 
 
 
and a parallelogram ABCD are standing on the same base AB and between the same parallels AB, DC.
 
 
 
 
Complete the parallelogram ABPQ.
 
 
 
 
 
The area of a triangle is half that of a parallelogram standing on equal bases and between the same parallels.
 
 
 
 
 
Triangles on the same base and between the same parallels are equal.
 
 
 
and are on the same base and between the same parallels AB, DQ.
 
 
 
 
Complete the parallelograms ABCD and ABPQ.
 
 
 
 
Triangles with equal areas on the same base have equal corresponding altitudes.
 
 
 
and are equal in area and are on the same base AB. PM and QN are altitudes.
 
 
PM = QN
 
 
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