Posted by **Emily** on Sunday, November 1, 2009 at 5:51pm.

I need help on a geometry proof!!!!

If Line AB is parallel to Line DC and Line BC is parallel to line AD, prove that angle B is congruent to angle D.

The picture is basically a square or parallelogram with line DC on the Top and Line AB on the bottom, and as u can tell A and D connect to form a line and C and B connect to form a line.

HELP I don't understand proofs at all, and have a test soon!!!!!!!!!!

- Geometry -
**Judy**, Sunday, November 1, 2009 at 6:16pm
Let ABCD be a quadrilateral such that the pair of opposite sides AB and CD are equal

and parallel to each other

We need to show that AD and BC are parallel to each other. Consider the two triangles ABD and CDB, we have

AB = CD (given)

ÚABD = ÚCDB (alt. int. Ús of // lines AB and CD)

BD = DB

Hence ƒ¢ABD ≅ ƒ¢CDB (S.A.S.)

and ÚADB =ÚCBD (corresponding Ús of congruent triangles) ˆ AD // BC (theorem 2.5(i):

converse of alt. int. Ús of // lines) This completes the proof of this theorem

- Geometry -
**Anonymous**, Wednesday, November 4, 2009 at 2:20pm
Indicate in standard form the equation of the line through the given points.

P(0, -4), Q(5, 1)

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