Sonta Murray

WRITE UP –2

June 4, 2003

 

 

 

 

PROBLEM:

 

 

E is a midpoint of side GO, and D is a midpoint of side RO. Explain why triangle GOR has the same area as rectangle MATH.

 

 

 

 

             

 

 

Solution: 

 

LINE SEGMENT ME IS CONGRUENT TO LINE SEGMENT  HE     -- CORRESPONDING SIDES ARE CONGRUENT

 

< E IS CONGRUENT TO <E     ----  VERTICAL <’S ARE CONGRUENT

 

< H IS CONGRUENT TO < M CORRESPONDING RIGHT <’S ARE CONGRUENT

 

 

THEREFORE TRIANGLE GEH IS CONGRUENT TO TRIANGLE OEM  ----ASA

 

 

< D IS CONGRUENT TO < D- VERTICAL <’S ARE CONGRUENT

 

LINE SEGMENT AD IS CONGRUENT TO LINE SEGMENT TD  --CORRESPONDING <’S ARE CONGRUENT

<A IS CONGRUENT TO < T   ----CORRESPONDING <’S ARE CONGRUENT

 

THEREFORE TRIANGLES ADO AND TDR ARE CONGRUENT  ------- ASA

 

AS A RESULT, THE AREA OF BOTH FIGURES ARE EQUAL.