Is all rhombi have four congruent angles?

Question

I need to identify the statement which is false. Explain with words and /or pictures why it is false. Correct the statement so that it is true.

Answer 1

first, the definition of a rhombus:

http://en.wikipedia.org/wiki/Rhombus

 

It is a parallelogram in which all 4 sides are equal.  Looking at the pictures in the Wikipedia article, we see that opposite angles will be congruent.

 

(a square is a special case of a rhombus---in a square all 4 angles are congruent)

 

The correct statement:

"All rhombi have 2 pairs of congruent angles"

Answer 2

A rhombus is a quadrilateral whose sides are equal in length all around, but they have 2 pairs of congruent angles.  Think of a square which has sides of equal length and angles of equal measure at all corners, but the opposite sides of that square are tilted.  This means that one angle will be larger or smaller than another angle.  You know that the sum of the angles of a quadrilateral is 360 degrees.

 

A square has 4 angles that are each 90 degrees. 

90 + 90 + 90 + 90 = 360.

 

If rhombus has two angles that are 80 degrees equally, then the other two angles are 100 degrees equally. 

80 + 80  100 + 100 = 360

 

Answer 3

A rhombus can have four congruent angles. It is called a square.