Congruence and Similarity

New Zealand

Level 6 - NCEA Level 1

Lesson

The sides lengths of similar shapes are in the same ratio or proportion. So once we know that two shapes are similar, we can solve any unknown side lengths by using the ratio.

Remember!

You can write the ratio of the big triangle to the little triangle or the little triangle to the big triangle. This is helpful as it means you can always have the unknown variable as the numerator.

Find the value of $u$`u` using a proportion statement.

Think: Let's equate the ratios of matching sides.

Do:

$\frac{u}{14}$u14 |
$=$= | $\frac{3}{21}$321 | |

$=$= | $\frac{1}{7}$17 | (Multiply both sides by $14$14) | |

$u$u |
$=$= | $\frac{1\times14}{7}$1×147 | (Now let's simplify) |

$=$= | $\frac{14}{7}$147 | (Keep going!) | |

$u$u |
$=$= | $2$2 |

Consider the two similar triangles.

Solve for $x$

`x`.Solve for $c$

`c`.

A $4.9$4.9 m high flagpole casts a shadow of $4.5$4.5 m. At the same time, the shadow of a nearby building falls at the same point (S). The shadow cast by the building measures $13.5$13.5 m. Find $h$`h`, the height of the building, using a proportion statement.

Recognise when shapes are similar and use proportional reasoning to find an unknown length

Apply geometric reasoning in solving problems