Finding the order of rotational symmetry Congruent shapes

Finding the order of rotational symmetry

Congruent shapes If shapes are identical in shape and size then we say they are congruent. Congruent shapes can be mapped onto each other using translations, rotations and reflections. These triangles are congruent because B P C A AB = PQ, BC = QR, and AC = PR. A = P, B = Q, R Q and C = R.

There are four ways to show the a pair of triangles are congruent: Method One: If the three sides are equal SSS rule. Method Two: Two sides and the included angle are equal SAS Angle must be between the two sides Method Three: Two angles and the corresponding side ASA The side does not need to be between the two angles Method Four : Right angle hypotenuse and one side RHS

Congruence and similarity Is the image of an object that has been enlarged congruent to the object? Remember, if two shapes are congruent they are the same shape and size. Corresponding lengths and angles are equal. In an enlarged shape the corresponding angles are the same but the lengths are different. The image of an object that has been enlarged is not congruent to the object, but it is similar. In maths, two shapes are called similar if their corresponding angles are equal and their corresponding sides are different but in the same ratio.

Find the scale factor What is the scale factor for the following enlargements? B’ B Scale factor 3 To calculate the scale factor = New length Original/Old length

Find the missing lengths The second photograph is an enlargement of the first. What is the length of the missing side? 10 cm 4 cm 3 cm ? 7. 53 cm

Find the missing lengths The second photograph is an enlargement of the first. What is the length of the missing side? 10 cm 4 ? cm 5 cm 12. 5 cm

Find the missing lengths The second picture is an enlargement of the first picture. What are the missing lengths? 11. 2 cm 5. 6 cm cm 6. 7 ? 6. 7 cm 13. 4 cm 2. 9 cm 5. 8? cm

Find the missing lengths The second shape is an enlargement of the first shape. What are the missing lengths? 6 cm 44 cm ? cm 4. 5 ? cm 3 cm 9 cm 6 cm 55? cm cm 7. 5 cm

Find the missing lengths The second cuboid is an enlargement of the first. What are the missing lengths? 10. 5 cm 3. 5 ? cm 3. 5 1. 8 cm 1. 2 cm 3. 6 ? cm 5. 4 cm