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!!!!!!!!!!

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

Indicate in standard form the equation of the line through the given points.

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

Sure, I'd be happy to help you with your geometry proof!

To prove that angle B is congruent to angle D, we can use the fact that Line AB is parallel to Line DC and Line BC is parallel to Line AD. These parallel lines create pairs of corresponding angles.

Here's a step-by-step explanation of how to prove this:

Step 1: Start by drawing a diagram of the given information. Label points A, B, C, and D in the diagram.

Step 2: Write down the given information, which is that Line AB is parallel to Line DC and Line BC is parallel to Line AD.

Step 3: Identify the pairs of corresponding angles created by the parallel lines. In this case, the pair of corresponding angles we are interested in are angle B and angle D.

Step 4: Write down the statement that angle B is congruent to angle D. You can write this as "∠B ≅ ∠D" or "angle B is congruent to angle D."

Step 5: To prove that angle B is congruent to angle D, we can use the Corresponding Angles Postulate, which states that if two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent.

Step 6: Write down the Corresponding Angles Postulate, which is "If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent."

Step 7: Since Line AB is parallel to Line DC and Line BC is parallel to Line AD (given information), we can conclude that angle B and angle D are corresponding angles.

Step 8: Now, write down the statement that "by the Corresponding Angles Postulate, angle B is congruent to angle D."

Step 9: Finally, include a reasoning statement, which is a brief explanation of why the previous statement is true. In this case, you can write "since angles B and D are corresponding angles formed by parallel lines AB and DC, by the Corresponding Angles Postulate, they are congruent."

And that's how you can prove that angle B is congruent to angle D using the given information and the Corresponding Angles Postulate.

I hope this helps! Let me know if you have any further questions.

How to find the length of EC

Give your answer to the nearest cm