Question

Will give medal for help.
Prove that opposite sides of a parallelogram are congruent. Be sure to create and name the appropriate geometric figures.

Answer 1

By Parallelogram definition, line AB is parallel to line CD and line BC is parallel to line DA.

We are required to prove that AB = CD and BC = DA.

Let AC be the diagonal of parallelogram.

Consider two Triangles ABC and CDA as shown in figure.

In triangles,

1. +Angle+CAB+=+Angle+ACD .....(The line AC is a transversal of parallel lines AB and CD,hence Angle CAB and ACD are alternate angles)

2. Angle+ACB+=+Angle+CAD .....(The line AC is a transversal of parallel lines BC and DA,hence Angle ACB and Angle CAD are alternate angles)

3. AC+=+CA ......(The common side to two triangles)

From conditions 1,2 and 3,

Triangles ABC and CDA are congruent (By Angle -Side-Angle congruency property)

Hence as triangles are congruent triangles , the corresponding sides are equal,

so AB = CD and BC = DA.
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Answer 2

thank you SO much

Answer 3

welcome

Answer 4

would you mind helping with one more

Answer 5

no

Answer 6

tell me

Answer 7

Prove that the base angles of an isosceles triangle are congruent. Be sure to create and name the appropriate geometric figures.