Embedded Files
Introduction
Introduction
You will be finding different angles in a triangle in this lesson. What do you know about the sum of angles in a triangle? Take a look at this video to find out.
Look at the shapes at the right:
Can you find the angles at the centre of the shapes? If you need a hint, look at this video about angles around a point.
What types of triangles do we have here?
Can we find all angles on the right? If you need a hint, look at this video about finding angles of isosceles triangles.
Now take a look at the triangle on the 9 pin geoboard on the right:
How many different triangles from the centre can you make? Use this template (PRINT ME) or this virtual geoboard on nRich to draw all of them. Don't forget to take screenshots and put them on a Google Doc as evidence.
If you are unsure how to start, look at this video.
What types of triangles do we have here?
How do you know you have all of them?
Work out all the angles of your triangles. You can use this to check your answers are correct.
Now take a look at the second triangle on the 9 pin geoboard on the right:
How many different triangles can you make if you can NOT use the centre pin? Use this template (PRINT ME) or this virtual geoboard on nRich to draw all of them. Don't forget to take screenshots and put them on a Google Doc as evidence.
What types of triangles do we have here?
How do you know you have all of them?
Work out all the angles of your triangles. You can use this to check your answers are correct.
Further Questions and Challenges
Further Questions and Challenges
Can you come up with a coding system to record results and avoid repetition?
Can you now repeat the above with geoboards with different number of pins e.g. 10, 12, 5, 6? Use this virtual geoboard
How many different triangles i) from the centre ii) without the centre pin can you make?
What types of triangles do we have here?
How do you know you have all of them?
Work out all the angles of your triangles. You can use this to check your answers are correct.
Can you come up with a rule that links number of dots on the circumference with the number of triangles that can be made?
Now go back to a 9 pin geoboard and explore producing a quadrilateral (4 sided shape):
How many different quadrilaterals i) from the centre ii) without the centre pin can you make?
How do you know you have all of them?
Work out all the interior angles of your quadrilateral. Hint: you can do that by combining different triangles.
You can use this to check your answers are correct.
Now repeat the above by exploring different polygons e.g. pentagon (5 sided shape), hexagon (6 sided shape) etc.
Can you come up with a rule that links number of sides a polygon has with the sum of interior angles?
Can you come up with a rule that links number of dots on the circumference with the order of rotational symmetry different regular polygons have?
Click on the hyperlinks if you don't know what order of rotational symmetry or regular polygons mean.
Further Practice
Further Practice
Consolidate your understanding on finding angles in a triangle by doing the relevant skills practice onDrFrostMaths, CorbettMaths, MyiMaths and Eedi. Watch any video and/or go through any online lesson as you see fit. Here are some further self-marked practices on transum:
Angle Theorems - this is not a practice exercise, it simply lists out all the theorems you need to know. You will learn about the the last 2 in Year 8.
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