Maths - Similarity

• What does it mean to enlarge a shape?


  To make a shape bigger (or smaller) by a given multiplier (scale factor)
• What is the centre of enlargement?


  The point the shape is enlarged from
• What does it mean for shapes to be similar?

  One shape can become another with a reflection, rotation, enlargement, or translation
• What does it mean for shapes to be congruent?


  They are the same size and shape
• What does "corresponding" refer to in geometry?


  Items that appear in the same place in two similar situations
• What are parallel lines?


  Straight lines that never meet (equal gradients)
• What should you be able to do by the end of the unit on similarity?


  • Enlarge by a positive scale factor
  • Enlarge by a fractional scale factor
  • Identify similar shapes
  • Work out missing sides and angles in similar shapes
  • Use parallel lines to find missing angles
  • Understand similarity and congruence
• What happens to angles in similar shapes?


  Angles do not change
• If shape A is enlarged by a scale factor of 2 from (0,0), what happens to the distance from the point?


  The distance from the point enlarges by 2
• What effect do fractional scale factors have on shapes?


  Fractions less than 1 make a shape smaller
• How do you identify similar shapes using side lengths?


  By comparing the ratios of corresponding sides
• What is the scale factor if the sides of a larger shape are 1.5 times bigger than the smaller shape?


  1. 5
• What is the relationship between corresponding angles in similar shapes?


  Corresponding angles are equal
• How can you calculate missing angles using parallel lines?


  By applying alternate and corresponding angle rules
• What are the conditions for congruent triangles?


  • Shares a vertex
  • All angles are the same
  • All corresponding sides are the same size
• What is the significance of vertically opposite angles in triangles?


  They are equal
• What are the conditions for triangles to be congruent?


  • Side-side-side (SSS)
  • Angle-side-angle (ASA)
  • Side-angle-side (SAS)
  • Right angle-hypotenuse-side (RHS)
• What is the Pythagorean theorem?


  $c^2 =$$a^2 +$$b^2$ where $c$ is the hypotenuse
• What is the hypotenuse in a right-angled triangle?


  The longest side opposite the right angle
• What is the tangent ratio?


  The ratio of the length of the opposite side to that of the adjacent side
• What is the sine ratio?


  The ratio of the length of the opposite side to that of the hypotenuse
• What is the cosine ratio?


  The ratio of the length of the adjacent side to that of the hypotenuse
• What is an inverse function?


  A function that has the opposite effect
• What should you be able to do by the end of the unit on trigonometry?


  • Work fluently with hypotenuse, opposite, and adjacent sides
  • Use the tan, sine, and cosine ratios to find missing side lengths
  • Use the tan, sine, and cosine ratios to find missing angles
  • Calculate sides using Pythagoras’ Theorem
• How do you label the sides of a right-angled triangle?


  Hypotenuse, opposite, and adjacent
• What is the relationship between the sides of a right-angled triangle when the angle is the same?


  The ratio of sides remains the same
• How do you use the tangent ratio to find a missing side?


  By rearranging the formula $\tan \theta =$$\frac{\text{opposite}}{\text{adjacent}}$
• How do you use the sine ratio to find a missing angle?


  By using the formula $\sin \theta =$$\frac{\text{opposite}}{\text{hypotenuse}}$
• How do you use the cosine ratio to find a missing side?


  By using the formula $\cos \theta =$$\frac{\text{adjacent}}{\text{hypotenuse}}$
• What is the significance of key angles in trigonometry?


  They provide specific ratios for sine, cosine, and tangent
• What is the value of $\tan 0°$?


  0
• What is the value of $\sin 90°$?


  1
• What is the value of $\cos 0°$?


  1
• What is the value of $\tan 90°$?


  Undefined
• What is the value of $\sin 0°$?


  0
• What is the value of $\cos 90°$?


  0
• Similar triangles have the same shape but not necessarily the same size.