SOLUTION: In a triangle congruence proof, it shows to two triangles abm and dem vertically up and down and the given is m is the mid point of line segment ae and line segment cd and you have
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-> SOLUTION: In a triangle congruence proof, it shows to two triangles abm and dem vertically up and down and the given is m is the mid point of line segment ae and line segment cd and you have
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Question 311409: In a triangle congruence proof, it shows to two triangles abm and dem vertically up and down and the given is m is the mid point of line segment ae and line segment cd and you have to prove line segment ab and line segment de paralell how do you prove them paralell in a two column proof? Answer by mollukutti(30) (Show Source):
You can put this solution on YOUR website! The diagram is possible only if cd is bd. Let us assume that the actual line segment is bd and that cd is a typo error.
On drawing the diagram we will get two triangles joining at m
Proof:
Proof of congruence of the triangles dem and abm
dm=mb (m is the mid point of db)
em=ma (m is the mid point of ae)
The included angle dem = included angle bma (vertically opposite angles)
Therefore the triangles dem and abm are congruent which means the remaining sides de and ab are also equal.
Angles contained by equal sides are equal
Therefore the angle mde = angle mba
But these are alternate angles
Hence the sides de and ab are parallel to each other (Going by the theorems of paralles lines and the angles formed with an intersecting line)
