Question

Quadrilateral ABCD has congruent angles and opposite sides that are congruent. What classification can be given to ABCD?

Parallelogram

Rectangle

Rhombus

Square

Answer 1

@mathmate This is really confusing because can't there be more than one answer

Answer 2

There is the x and the y-coordinates to calculate, which makes an ordered pair.
An ordered pair always has two numbers, such as D(-3,-3).

Answer 3

Ok, but how do i use that to classify what this question asks @mathmate

Answer 4

Oh, my. I answered in the wrong place! Sorry.
Here you are looking at quadrilaterals that satisfy all the conditions.
1. all angles are congruent.
Can it be a parallelogram?
Can it be a rhombus?
Can it be a square?
Can it be a rectangle?
Those which cannot be, reject.
Proceed to condition 2.
Are the opposite sides parallel?
Can it be a parallelogram?
Can it be a rhombus?
Can it be a square?
Can it be a rectangle?
Those choices which satisfy both conditions is/are your answer.

Answer 5

Sorry, the second condition is "are opposite sides congruent?"

Answer 6

haha no problem! :)

so for #1, I would reject rectangle and parallelogram, right?
and for #2 I can cross out which ones?

Answer 7

I picked my answer to be square, is that right?

Answer 8

Not really.
A rectangle has all angles 90 degrees, so cannot reject.
I think all remaining figures satisfy condition 2.
So you should be left with two choices which have all angles congruent.

Answer 9

so rhombus

Answer 10

sorry, I mean rectangle

Answer 11

@mathmate

Answer 12

Rectangle is good.
What's the other one?

Answer 13

Rhombus?

Answer 14

Do all rhombuses have all angle equal?

Answer 15

umm nope

Answer 16

parallelogram? lol sorry, i know im horrible haha

Answer 17

You are looking for 2 shapes from the list that have ALL angles equal.
In fact, you have mentioned it as a choice at the very beginning.

Answer 18

square and rectangle are the two choices.

Answer 19

Since they both contain 4 right angles.

Answer 20

So out of those two, we need to find out which have opposite sides that are congruent

Answer 21

right

Answer 22

Rectangle and square are both correct.
You may notice that all the four shapes (rectangle, square, rhombus and parallelogram) have opposite equal, so condition 2 does not do much.

Answer 23

Oh right :/ but we are only down to 2 options though right? because of condition 1

Answer 24

or not..

Answer 25

That's right.
So you have two choices for your answer.

Answer 26

So does that mean that either one will be correct? :???

Answer 27

Let me read the question again if only one answer is permitted.

Answer 28

Mhm, thank you. :)

Answer 29

That's right, either one is a good answer, or both.

Answer 30

ok, thank you!

Answer 31

If the question had been "... adjacent sides are equal, ", then only square will qualify.

Answer 32

You're welcome!