Year 9 Engineering Geometry: Similarity and Pythagoras' Theorem

Vocabulary and essential concepts from the Year 9 Engineering Geometry Practice Test covering similarity tests, Pythagoras' theorem, and scale factors.

Hypotenuse

The longest side of a right-angled triangle, located directly opposite the right angle.

Pythagoras' Theorem

The formula used to find missing side lengths in right-angled triangles, expressed as $a^2 + b^2 = c^2$ where $c$ is the hypotenuse.

AA Similarity Test

A test to prove two triangles are similar if two corresponding angles are equal (which implies the third angle must also be equal).

SSS Similarity Test

A test to prove similarity where the ratios of all three corresponding side pairs are equal, such as $10/4 = 15/6 = 20/8 = 2.5$.

SAS Similarity Test

A test to prove similarity where two pairs of corresponding sides are in the same ratio and their included angles are equal.

Scale Factor

The value calculated by dividing a length in one similar shape by the corresponding length in the other, such as $15 \times 6 = 2.5$.

Similarity Statement

A mathematical notation using the squiggle symbol ($\sim$) to show two shapes are similar with vertices in corresponding order, such as $ABC \sim DEF$.

Scale (e.g., 1:20)

A ratio used in engineering drawings where $1$ unit of measurement on the model or drawing represents a specific number of units (e.g., $20$) on the full-size object.

Verification of a Right Angle

The process of checking if the squared sum of the two shorter sides equals the square of the longest side ($a^2 + b^2 = c^2$); if equal, the triangle is right-angled.

$$12^2$$

The square of $12$, which equals $144$.

$$17^2$$

The square of $17$, which equals $289$.

$$\sqrt{196}$$

The square root of $196$, which equals $14$.

$\sqrt{70}$ (to 1 decimal place)

The square root of $70$, approximately equal to $8.4$.

Metric Conversion: Centimetres to Metres

The process of dividing a length in centimetres by $100$ to find the equivalent length in metres, such as $320\,cm = 3.2\,m$.

Corresponding Sides

Pairs of sides that occupy the same relative position in two similar figures, such as side $AB$ in triangle $ABC$ matching side $DE$ in triangle $DEF$.