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Math Help - Congruent Triangles

  1. #1
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    Question Congruent Triangles

    In the figure given below, ABC is an isosceles triangle in which AB=AC. Also D is a point such that BD=CD. How do I prove that AD bisects angle A & angle D?

    This is what I have done:

    Consider the triangles ABD & ACD.

    AB=AC (given)
    BD=CD (given)
    AD=DA (common side)

    Thus the triangles ABD & ACD are congruent by Side-Side-Side (SSS) congruence rule but how do I prove that AD bisects angle A & angle D?

    Thanks,

    Ron
    Attached Thumbnails Attached Thumbnails Congruent Triangles-triangle.gif  
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  2. #2
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    Quote Originally Posted by rn5a View Post
    In the figure given below, ABC is an isosceles triangle in which AB=AC. Also D is a point such that BD=CD. How do I prove that AD bisects angle A & angle D?

    This is what I have done:

    Consider the triangles ABD & ACD.

    AB=AC (given)
    BD=CD (given)
    AD=DA (common side)

    Thus the triangles ABD & ACD are congruent by Side-Side-Side (SSS) congruence rule but how do I prove that AD bisects angle A & angle D?

    Thanks,

    Ron
    Since triangles ABD and ACD are congruent, it follows that "corresponding parts", such as angles BAD and CAD and angles BDA and CDA are congruent.

    Lable the point of intersection "P". Now clearly AP is a line in both triangle ABP and triangle ACP. Use SAS to prove those two triangles are congruent.

    Similarly, DP is a line in both triangle DBP and triangle DCP. Use SAS to prove those two triangles are congruent.
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