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

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)
RELATED QUESTIONS
How do I prove congruence of these 2 triangles in a 2 column proof. I am given a picture... (answered by rothauserc)

Please help me solve the following proof: The directions are: Draw and label a... (answered by stanbon)

Need help answering please? Study the flow proof for a leg-leg (LL) Congruence... (answered by MathLover1)

i have a parallelogram question but i can not copy paste or snapshot it i will try to... (answered by josgarithmetic)

Please help me solve this proof- Use the definition of angle congruence to prove that... (answered by richard1234)

The ABM Coffee Company claims that 20% of the coffee drinkers in Pinalagad, Malinta... (answered by Boreal)

(Please help) Find as many congruent triangles as possible. State a congruence... (answered by ikleyn)

Problem 4: Find as many congruent triangles as possible. State a congruence statement for (answered by ikleyn)