The total sum of the interior angles in a triangle is...

A right angled triangle with one angle as 23 degrees would mean the remaining interior angle would be...

In an equilateral triangle, each interior angle would be equal to...

If a base angle of an isosceles triangle was 34 degrees, what would the other base angle be?

If the base angles of an isosceles triangle were 34 degrees, what would the unknown angle be?

Interior angles in triangles:

﻿Hello, and welcome to this online lesson about angles and polygons: categorising and defining polygons. Please take a moment to clear away any distractions, such as your brother, your sister, your pet, whatever may be distracting you this moment in time, right, and then find a quiet place where you're not going to be disturbed whatsoever, 'cause we really need to focus on the task at hand, okay. So make sure that your notifications for any apps is silenced whilst this is going on too. We're about to do some really powerful maths, and we wouldn't want to lose our thought midway through. I know for one it's really, really annoying when you just you're so close to getting the answer and you get distracted by a tiny, tiny little thing. So make sure, like I've got my phone on silent in the moment, make sure yours is on silent too. Or if you are using your device, make sure you've got all those app notifications, et cetera, turned off. So with that, let's go on. And what I'd like you to do is to attempt the, Try this. So have a go at sorting these shapes into groups. So think about what groups you could do for this. You could, for example, sort them by ones that have right angles, for example. Okay. So pause the video now and have a go at sorting those shapes. Fantastic. What groups did you get? Did you get, for example, the ones with the right angles? Did you get ones that were pentagons, for example? Did you get any sort of things? You know, there's so many different possibilities. There's quadrilaterals, those four-sided shapes. That's what we're going to explore today. So we're going to look at those sorts of shapes and think about how can we define them, play around with them, those sorts of things. So there's quite a lot of terminology we're going to use today. And these are the key points. So we have a polygon and that is a shape that's made up of three or more sides. We have an acute angle, which is an angle less than 90 degrees. A right angle, that is a 90 degree angle. An obtuse angle, an angle between 90 and 180 degrees. A reflex angle, an angle greater than 180 degrees. A concave angle. That may be one that you haven't necessarily heard before. That's an internal angle of a polygon. It's between 180 and 360 degrees. A convex angle is an internal angle of a polygon between 80 and 180 degrees. So it looks something like that. Whereas a concave angle would be looking something like that. A regular shape is a polygon with all sides of equal length. So an example would be for example any collateral triangle, a regular hexagon. And that's what we'd say, if all those sides are the same lengths. Congruent means that the shape is identical. It may have been reflected, rotated, or translated. Reflected meaning like a mirror line. Rotated meaning sort of rotated around a point. And translated means to have shifting units up and down on a Cartesian plane. A similar shape is a similar as a shape that has identical angles and sides in the same ratio. So a lot to take down there. I appreciate it is quite a lot. So if you need to make notes, by all means make the notes now. Excellent! So you've copied that down and we're ready to go. So what I'd like you to think about is how to categorise the following. So categorise those shapes in the Venn diagram there. So a hexagon has a concave angle, and if both those criteria are fulfilled, then of course it goes in that intersection, that middle point there. So think about whether or not that is true for all those shapes. Some of them may not be able to be placed in that Venn diagram at all. So just be very careful. Pause the video now and have a go at that task. Excellent! So this is what you should have got. We've got our answers here. Did you get those answers? If you did fantastic, really, really good work. I'm really impressed the work you do so far. You're keeping up and getting this. That's fantastic. Not many people know a huge amount about concave angles. So really good if you're able to get that and use that terminology correctly. Especially convex as well; concave, convex, et cetera. Okay. Now what I'd like you to think about now is the explore tasks. And I want you to think what shapes can be made by combining these equal length rods. It sounds quite easy in principle, and there are some really easy shapes that we can think of. Think of more complex shapes though if you can. Pause the video, and if you need help I'll be on the next slide. So I'm assuming you may need some support and that's absolutely fine. So if you do need some support, here it is. You can think of mainly regular shapes that can be formed. So for example, there I have a rhombus. Can you think of any others that you could maybe form as a result of that? you can maybe form a rectangle, right? You can have a rectangle with two rods at the top is the length. One is the width, two the bottom length there, and then one is the width, that would be fine. You could also make a square of course, where you have all those rods that are the same length there. I'm just giving you one possibility there. You can make an even bigger rhombus there which would be absolutely fine. So think about ones that you can play around with there, and what answers you can get as a result of doing that. So that brings us to the end of today's lesson. I just want to say you've done an amazing job if you're able to keep up with that. I'm sure you're on track to do really really well as time has gone on. So just remember, this is our second lesson so far that we've had. Join in for the third lesson. I'd be really, really happy and excited to see you. Remember that you can take a picture of your work that you've done today. As long as you ask your parent or carer and send it to @OakNational on Twitter. Hopefully then I'll even be able to see it. And I can revel in your success and see how well you've done. So I hope you've learned a lot in today's lesson. Please, please, please remember to that post-quiz. Really important that you're able to check the knowledge that you've learned today. This is goodbye from me, and I'll see you soon. Take care. Bye-bye.

Which of the following statements most accurately describes an 'obtuse angle'?

Which of the following statements most accurately describes an 'acute angle'?

Which of the following statements most accurately describes a 'regular polygon'

A rhombus is an example of a...

Another word for a regular quadrilateral would be...

Categorising and defining polygons

In this lesson, we will learn about the key terminology involved in describing polygons, and begin to categorise polygons, based on certain properties.

Maths

Y8 Maths

Key Stage 3

Year 8

Angles in polygons

Geometry

THEME

UNIT

Interior angles in a triangle

Building shapes from triangles (Part 1)

Building shapes from triangles (Part 2)

Polygons and triangles

Generalising angles in polygons (Part 1)

Generalising angles in polygons (Part 2)

Finding missing angles in polygons

Exterior angles

Regular interior and exterior angles (and mean of irregular)

Generalising and comparing generalisations

Angle notation and problem solving

Is it possible to have two obtuse angles in a triangle?

The total exterior angles of a polygon sum to...

The calculation to work out the sum of the interior angles for an octagon would be...

Squares tesselate with each other.

ABC is a triangle. Angle ABC is 90 degrees. Angle BAC is 23 degrees. Angle ACB is...

The mean interior angle of a quadrilateral is...

If I have a regular pentagon, what would the total interior angles sum to?

The general formula for working out the total interior angles in a n-sided polygon is...

Lesson overview:Categorising and defining polygons

Core Content

Angles in polygons: