Question

Quadrilateral ABCD has diagonals that are congruent and perpendicular to each other. What classification can be given to ABCD? (5 points)
Select one:
a. Parallelogram
b. Rectangle
c. Rhombus
d. Square

Answer 1

Did we meet before?

Answer 2

ummmm i think

Answer 3

Diagonals congruent: rectangle
Diagonals perpendicular: rhombus

Answer 4

Combine the two properties, what do you get?

Answer 5

ummm idk

Answer 6

Let me draw the "quadrilateral map" for you

Answer 7

ok

Answer 8

So what is both a rectangle and a rhombus?

Answer 9

is the answer A?

Answer 10

No, the relationship of a rectangle and a rhombus to a parallelogram from the map read that:
A rectangle and a rhombus are both a kind of parallelogram

Answer 11

It's like that parallelogram is the father of rectangle and rhombus

Answer 12

But I'm asking what is both a kind of rectangle and a kind of rhombus

Answer 13

Now think about it this way:
Rectangle is a quadrilateral with 4 right angles
Rhombus is a quadrilateral with 4 equal sides

Answer 14

So the thing that's both a kind of rectangle and a kind of rhombus would have 4 right angles and 4 equal sides...

Answer 15

Which is...?

Answer 16

so i had to go do something

Answer 17

DEFINITION OF QUADRILATERALS:
A kite is a quadrilateral with TWO pairs of ADJACENT sides that are CONGRUENT
A trapezium is a quadrilateral with ONLY ONE pair of PARALLEL sides
A parallelogram is a quadrilateral with TWO pairs of PARALLEL sides
A rectangle is a quadrilateral with four RIGHT angles
A rhombus is a quadrilateral with four EQUAL sides
A square is a quadrilateral with four RIGHT angles AND four EQUAL sides

Answer 18

srry i keep leaving my mother keeps calling my name

Answer 19

PROPERTIES OF QUADRILATERALS:
Parallelogram - opp sides eq, opp angles eq, diags bisect each other
Rhombus - all props of //gram, diags ⊥ with each other
Rectangle - all props of //gram, diags congruent
Square - all props of rhombus, all props of rectangle

Answer 20

so you are trying to ask me what is both a kind of rectangle and a kind of rhombus

Answer 21

Yes

Answer 22

i really dont get that question

Answer 23

@ganeshie8 @jim_thompson5910

Answer 24

Let me rephrase the question:
Which kind of quadrilateral has diagonals that are (a)congruent to each other and (b)perpendicular to each other?

Answer 25

So if a quadrilateral has diagonals congruent to each other, it's a rectangle (see properties listed above)
And if a quadrilateral has diagonals perpendicular to each other, it's a rhombus (see properties listed above)

Answer 26

Therefore that quadrilateral would be both a rectangle and a rhombus

Answer 27

would the answer be between C and D

Answer 28

And only a square is both a rectangle and a rhombus

Answer 29

Sacred pettering flullet

Answer 30

I'd say square is the only one to meet those requirements.
http://www.1728.org/quadltrl.htm