In trapezium ABCD, AB and CD are bases. Find AB if OD = 15cm, OB = 9cm, CD = 25cm.
| September 2, 2021 | education
Triangles AOB and COD are similar in two angles. The angle AOB is equal to the angle OCD as the vertical angles at the intersection of the diagonals. The angle ОВА is equal to the angle ОDС as criss-crossing angles at the intersection of the secant BD of parallel straight lines AB and CD.
From the similarity of triangles AB / CD = OB / OD.
AB = CD * OB / OD = 25 * 9/15 = 15 cm.
Answer: The length of the base AB is 15 cm.
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