There are triangles D DEC and D BEF and a parallelogram ABCD in the given figure. The congruence property of triangles to prove CD. We get from the parallelogram CD = AB. Then we use the given information. AF = 2 AB, in the quest to proceed.

Class: Grade 10

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Detailed Solution

ABCD is a parallelogram which means opposite sides are of equal length & opposite angles are equal.
E is the midpoint of BC = BE = CE. When DE & AB are extended they meet on a point F. quad RTP = AF = 2AB
From D DEC & D BEF Ð DEC & Ð BEF are vertically opposite to each other.
Ð DEC = Ð BEF (VOA)
The line BC cuts the parallel line DC & AF & creates alternate angles Ð DCE & Ð FBE. Ð DCE = ÐFBE (alternate angles are equal).
Ð CDE = Ð BFE, BE = CE, Ð DCE = Ð FBE.
(Bu AAS congruence).
CD = BF but from the parallelogram we have DC = AB. So BF = AB Now the point B on the line segment is AF.
So, AF = AB + BF
Putting the values BF = AB in above equation
AF = AB + BF = AB + AB = 2AB

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