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Question:

angeleyes93
angeleyes93
Student
High School - 10th Grade

geometry paragraph proofs

write a paragraph proof THIS ISNT GIVEN BUT E IS THE MIDPOINT

given ABCD is a rectangle

prove : ANGLE EDC is congruent to ANGEL ECD

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Posted by angeleyes93 on Wednesday November 4, 2009 at 9:09 AM and tagged with geometry, math.

Answers:

  1. neela
    neela Teacher
    Graduate School

    eNotes Editor

    Let ABCD be the rectangle, with vertices, A,B,C and D (in anticlockwise order ).

    Let E be the mid of AB.

    Consider the triangles AED and EBC:

    AD = BC , being the opposite sides of  the rectangle

    AE = EB, E is the mid point of AB.

    Angle EAD = angle EBC, as ABCD is a rectanle, each of its angle is right angle.

    Therefore, by the postulate of -side  included angle and side-

    Triangle EAD is congruent to triagle EBC. So, ED=EC. Therefore,triangle EDC is an isosceles triangle. So, the angle EDC = angle EDC.

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    Posted by neela on Wednesday November 4, 2009 at 9:34 AM