Determine the most precise name of the quadrilateral ABCD

Question

Determine the most precise name of the quadrilateral ABCD.

triangle ABC≅trangle ADC, AB≠BC

Answer 1

it could be a rectangle or it could be a parallelogram

a rectangle is a special parallelogram

seeing that no angles are mentioned, it is a parallelogram

Answer 2

ΔABC ≅ ΔADC means AB ≅ AD, BC ≅ DC, ∠B ≅ ∠D, ∠BAC ≅ ∠ACD. It follows that ∠CAD ≅ ∠ACB.

Thus, you can prove that AB ll DC and BC ll AD because alternate interior angles are congruent.

That means  the figure is a parallelogram. 

Answer 3

Hi Melisa from Los Angeles, Ca...hope you had a great day at school.

Okay...good Geometry questions. Glad you asked Wyzant. Now I'll give you a hint by helping you with a visual picture so you will see what your teacher is expecting you to understand, but won't answer the question for you. All you will need to do is draw a triangle with all EQUAL sides, label that triangle ABC[you should know the name of this special kind of triangle...equilateral triangle...RIGHT?]. Now, copy the same triangle, exactly the same, flip that triangle but keeping the BC sides touching each other. You should have a quadrilateral ABAC, rename the quadrilateral ABCD. Since the new quadrilateral is the same sides all the sides will be equal. This kind of quadrilateral has a special kind of name...called a what? I know you know this...okay here is a hint...it begins with a 'p'.

Now draw another triangle, this time with say one side a different length than the other 2 sides. Do the same thing like you did above, relabel to the quadrilateral ABCD...does it meet the restrictions of your problem

        ΔABC ≅ ΔADC    and AB ≠ BC

If you are still having problems with these problems, contact me on Wyzant