Classifying shapes by lines and angles | Math | 4th grade | Khan Academy

Which shape matches all three clues? So here we have three clues, and we want to see which shape down below matches all three of these statements.

So let's start with the first clue. The first clue says the shape is a quadrilateral; "quad" meaning four-sided. So looking down here at our shapes, let's see which ones match that first clue. Shape one has one, two, three, four sides, so it is a quadrilateral. Shape two has one, two, three, four sides, so it's also a quadrilateral. Shape three has one, two, three, four, five, six sides, so it is not a quadrilateral; it's a six-sided shape or a hexagon. So we can rule that one out. It doesn't match clue one, so there's no way it can match all three clues. Finally, shape four has one, two, three, four sides again, so it is also a quadrilateral.

After clue one, we still have three possible answers: this first shape, the second shape, and the fourth shape. All match clue one; they are all quadrilaterals.

Looking at clue two, it says our shape has no right angles. Right angles are also 90-degree angles. Right angles are 90-degree angles, and they look something like this. We often see them marked with a square in the middle because they are sort of like square angles. We can create a square from the opening that these angles form. So this is a right angle.

Looking now down at our shapes, we can see right away that shape one has two right angles. There's a square corner and another square corner. So this has right angles, but the shape we're looking for has no right angles, so we can rule this shape out. Shape two does not have any right angles; these are not squared-off corners. Same with shape four; no right angle. So both of those still match both clues one and two.

Now we have two shapes left. They're both quadrilaterals, and they have no right angles. Finally, our last clue: the shape has four sides. We knew that because it was a quadrilateral, and those sides are of equal length. That means each of the sides is the same length.

Looking at this first one that we have left, shape two, it looks like these sides on the ends are shorter than the sides going up and down, so it looks like they are not equal length. So we can rule this one out. But let's be sure this last one works here. These sides, the sides all look like they're the same length, but the way we can know for sure that they are is these tick marks.

Anytime you have these marks, it's saying that any side that has the same amount of marks is the same length. All four of these sides have exactly one tick mark, so they are all equal in length. So shape four matches all three clues: it is a quadrilateral, there are no right angles, and it has four sides of equal length.

So shape four is our answer.