Similar triangles
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This document provides instructions for classifying and analyzing a set of 24 triangles. Students are asked to group the triangles based on similarities and differences in shape, and to identify if any are enlargements of each other. They are then instructed to calculate scale factors between enlarged triangles, find missing lengths, and use properties like Pythagorean theorem and cosine rule to determine right angles, areas, and area scale factors. The goal is for students to systematically analyze and compare the given set of triangles.
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Similar triangles
- 1. 1 息 Jim Noble, InThinking www.teachmaths-inthinking.co.uk Similar Triangles Classify 1 Take the pack of 24 triangles and put them into groups that are somehow different from each other. Record the letters of the shape in each group below and explain the means by which they were divided. Classify 2 Take the pack of 24 triangles and put them into different groups that are somehow different from each other. Record the letters of the shape in each group below and explain the means by which they were divided.
- 2. 2 息 Jim Noble, InThinking www.teachmaths-inthinking.co.uk Triangle Types Discussion - Is it possible to split the triangles up in to equilateral, isosceles, right- angled and scalene? What are the issues that come up when trying to do this? Enlargements Are any of the triangles enlargements of each other? Classify the triangles by this means (i.e. all triangles in a given group are enlargements of each other). Write down the letters of the triangles in the groups below.
- 3. 3 息 Jim Noble, InThinking www.teachmaths-inthinking.co.uk Scale factors Having decided on the groups above, consider the scale factors that enlarge each triangle to the other within the group. Note some down, for example, you might say that to enlarge triangle X to become triangle Y, the scale factor would be 3. You could write this down as X Y, scale factor 3. Make at least 10 similar statements below.
- 4. 4 息 Jim Noble, InThinking www.teachmaths-inthinking.co.uk Missing Lengths What are the missing lengths? How do you calculate these? For each set of 3 triangles there are 4 missing lengths. Each can be calculated in different ways. Pick one of the groups of three triangles and show below how you calculated the missing lengths.
- 5. 5 息 Jim Noble, InThinking www.teachmaths-inthinking.co.uk Extensions Try these now or keep them for - Use Pythagorass theorem to establish which of the triangles have right angles. - What are the areas of these triangles? - Investigate the area scale factors between these triangles. - Calculate all the angles in the other triangles using the cosine rule. - Now work out the areas of the other triangles. - Now investigate the area scale factors between these triangles as well. 1
- 6. 5 息 Jim Noble, InThinking www.teachmaths-inthinking.co.uk Extensions Try these now or keep them for - Use Pythagorass theorem to establish which of the triangles have right angles. - What are the areas of these triangles? - Investigate the area scale factors between these triangles. - Calculate all the angles in the other triangles using the cosine rule. - Now work out the areas of the other triangles. - Now investigate the area scale factors between these triangles as well. 1