Need to Know
Geometry
The rules you must have ready for the exam.
How to use this: say each rule in your head, then tap Show me to check.
Angles
3 rulesRule 01
Straight line.
Angles on a straight line add up to $180^\circ$.
Rule 02
Vertically opposite.
When two lines cross, opposite angles are equal.
Rule 03
Corresponding & alternate.
Across parallel lines: corresponding angles (F-shape) are equal; alternate angles (Z-shape) are equal.
Triangles
4 rulesRule 04
Angle sum.
The three angles of a triangle add up to $180^\circ$.
Rule 05
Exterior angle.
An exterior angle equals the sum of the two interior angles opposite it.
Rule 06
Isosceles.
Two equal sides give two equal base angles.
Rule 07
Equilateral.
All sides equal; all angles $60^\circ$.
Pythagoras
2 rulesRule 08
The theorem.
In a right-angled triangle, $H^2 = O^2 + A^2$ ($H$ is the hypotenuse, opposite the right angle).
Rule 09
Finding a shorter side.
Rearrange: $O^2 = H^2 - A^2$.
Circles
5 rulesRule 10
Parts.
Radius, diameter ($D = 2r$), chord, arc, sector, tangent, circumference.
Rule 11
Tangent and radius.
A tangent meets the radius at the point of contact at $90^\circ$.
Rule 12
Chord bisected.
A radius perpendicular to a chord cuts it exactly in half.
Rule 13
Angle in a semicircle.
An angle standing on the diameter is $90^\circ$.
Rule 14
Two radii.
Two radii form an isosceles triangle (equal base angles).
Enlargements & similar triangles
3 rulesRule 15
Scale factor.
$|A'B'| = k\,|AB|$. $k>1$ bigger, $k<1$ smaller. Area of image $= k^2 \times$ area of object.
Rule 16
Similar triangles.
Equal angles ⇒ equal side ratios: $\dfrac{a}{p} = \dfrac{b}{q} = \dfrac{c}{r}$.
Rule 17
Line parallel to the base.
It splits the two sides in the same ratio.
Mathslive.ie · Geometry · Need to Know