Join dots on the grid to make a quadrilateral that has three acute angles.
To help us answer the question, we’ve been given a five-by-five dotty grid. And the question asks us to join dots on the grid to make a quadrilateral. What is a quadrilateral?
Many words that start with the letters q-u-a come from the Latin. And they’re all to do with the number four. So we might think of the word “quarter,” which is one whole split into four equal parts, or maybe a quad bike, which has four tyres, quadriceps, which are four muscles on the front of our thigh. And so when we’re faced with the word “quadrilateral,” we know that it’s got something to do with the number four. In fact, “lateral” comes from a word that means sides. And so a quadrilateral is a shape with four sides. A square is a quadrilateral, and a rectangle and a rhombus and a kite and a parallelogram.
So we’re told to join dots on the grid to make a four-sided shape. But we’re told something about that four-sided shape. It has three acute angles. Let’s remind ourselves what the word “acute” means. A right angle is a square angle, 90 degrees. And an acute angle is any angle that’s less than a right angle, less than 90 degrees.
So we’re looking to draw a four-sided shape that has three angles that are less than right angles. Before we start, let’s remind ourselves that a quadrilateral, because it has four sides, must also have four vertices or four corners. So we’re looking to connect up four dots together. There are lots of different ways we could answer this question. So let’s just go through one of them.
Let’s start with this dot here. Where could we join this dot to so that we make an acute angle? Well, we can’t draw two lines away from it like this because this makes a right angle. The same is true if we connect them up this way. And if we turn our heads, we can see that this makes a right angle too. So we need to draw our line to further up the grid to make sure that we make a nice tight corner.
What if we draw a line up to this dot here, remembering of course to use a ruler as we do so? So we make the line nice and straight. We can do the same on the opposite side of the grid. We’ve drawn our first angle. And if we look carefully, we can see that this angle is less than 90 degrees. It’s less than a right angle.
A good way to check for right angles if we don’t have a protractor or angle measurer is to use the corner of a piece of paper. If it fits perfectly, it’s 90 degrees. But we can see that this angle is less than 90 degrees. It’s our first acute angle.
We’ve already got two of the sides to our shape. And so now we just need to draw two lines from these two points here. Which of the points on the top row should we connect up? If we connect to this corner point, we can see that this angle is acute. Unfortunately, this angle is more than 90 degrees. So it’s not acute. And this angle is acute. It’s less than 90 degrees. And so we’ve made a quadrilateral with three acute angles.
As we said at the start, there are several ways to answer this question. So let’s just show some of the other options. One, two, three acute angles; one, two, three acute angles. And if we turn our head slightly, we might be able to recognise the name of this shape. This is a kite.
There are lots more ways that we can answer this question. So rather than give one single answer, we’re going to think about the rule that will make your answer correct. Firstly, your shape must have four sides, which means that you need to connect up four dots. And those dots need to be connected with straight lines. So use a ruler. One, two, three, four. And also your shape must have three angles that are less than 90 degrees. One, two, and three. And remember, wherever you are in the world, you’ve always got a right angle measurer to hand to check your answer. You just need to use the corner of a piece of paper.