Geometry - Column 2

[user1454]

Hello, I have two questions:

1. Why is the option “Kite is a rhombus” not correct as well? Since all sides of a rhombus are equal, it could be interpreted that every pair of adjacent sides is also equal. I would greatly appreciate it if you could provide a clear explanation for this.
   

   

2. I completed this exercise correctly but wanted to confirm my solution. In a parallelogram, the area is calculated as base × height. The height must clearly be less than 4 and 5 because, in the triangle formed after drawing the height, the hypotenuse is either 4 or 5. Since the height is the side opposite an acute angle, it must be shorter than the hypotenuse. Therefore, given that the area of a rectangle is 4 × 5, for the parallelogram, the area would be 4 × (x < 5) or 5 × (x < 4), where x represents a value less than 4 and 5. Obviously, the area of the parallelogram would be less than 4 × 5.
   

   

[Leaderboard]

@user1454

Since all sides of a rhombus are equal, it could be interpreted that every pair of adjacent sides is also equal

You’re looking at this the other way round. Given a kite, does it have to be a rhombus?

And your second solution is OK.

[user1454]

Hi,

However, it could be a rhombus. The question does not specify whether it is asking “which one must be true” or “which one could be true.” Therefore, how can we determine that it implies “must be,” as you have pointed out?

Could you also provide a clearer explanation as to why the statement “A kite has at least two equal angles” is correct?

[Leaderboard]

@user1454

However, it could be a rhombus. The question does not specify whether it is asking “which one must be true” or “which one could be true.” Therefore, how can we determine that it implies “must be,” as you have pointed out?

“is” ~ must.

@user1454

Could you also provide a clearer explanation as to why the statement “A kite has at least two equal angles” is correct?

Sketch an example of a kite, carefully labelling the equal pairs of sides.