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Math Help - Parallelogram (2)

  1. #1
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    Parallelogram (2)

    In the figure , ABCD is a parallelogram . AE=BF and C is parallel to FH . Prove that

    (1) EFCD is a parallelogram
    (2) GHFC is a parallelogram
    (3) parallelogram GHFC and ABCD are equal in area

    My work :

    (1) BC // AD , AE=BF , AD=BC

    \angle ADE =\angle CBF (corresponding angle)

    \triangle ADE congruent to \triangle BCF

    \angle DEA =\angle CFB

    DE// CF , AF// DC

    Hence , EFCD is a paralleogram

    (2) DH // CF , CG//HF

    Hence , GHFC is a parallelogram .

    (3) not really sure .
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  2. #2
    MHF Contributor
    Grandad's Avatar
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    Hello thereddevils

    Comments below.
    Quote Originally Posted by thereddevils View Post
    In the figure , ABCD is a parallelogram . AE=BF and C is parallel to FH . Prove that

    (1) EFCD is a parallelogram
    (2) GHFC is a parallelogram
    (3) parallelogram GHFC and ABCD are equal in area

    My work :

    (1) BC // AD , AE=BF , AD=BC

    \angle ADE =\angle CBF (corresponding angle) No. You mean \color{red}\angle DAE=\angle CBF

    \triangle ADE congruent to \triangle BCF

    \angle DEA =\angle CFB

    DE// CF , AF// DC

    Hence , EFCD is a paralleogram. Apart from that this is fine.

    (2) DH // CF , CG//HF

    Hence , GHFC is a parallelogram . OK.

    (3) not really sure .Use the result from your previous post: parallelograms on the same base and between the same parallels are equal in area. Look first at CFDE and CFGH; then at CDEF and CDAB. (Note the bold type.)
    Grandad
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