Geometric Reasoning

Vertically opposite angles are equal
(vert opp ∠s)

Adjacent angles on a straight line add to 180° (Adj, ∠s on str. line)

Angles at a point add to 360°
(∠s at pt)

Angles in a triangle add to 180°
(∠ sum of Δ)

The exterior angle of a triangle equals the sum of the two interior opposite angles (ext ∠ of Δ)

The base angles of an isosceles triangle are equal (base ∠s isos. Δ)

Corresponding angles on parallel lines are equal (corresp ∠s, || lines)

Alternate angles on parallel lines are equal (alt. ∠s, || lines)

Co-interior angles on parallel lines add to 180° (co-int ∠s, // lines)

The interior angles of a polygon add to 180(n - 2)°, where n is the number of sides (int ∠ sum of polygon)

The exterior angles of a polygon add to 360° (ext ∠ sum of polygon)

Base isosceles triangle, equal radii
(base ∠s isos Δ, = radii)

The angle at the centre is equal to twice the angle at the circumference on the same arc (∠ at centre)

Angles on the same arc are equal
(∠s on same arc)

The angle in a semicircle is a right angle
(∠ in semicircle)

Opposite angle of a cyclic quadrilateral add to 180°
(opp ∠s, cyclic quad)

The exterior angle of a cyclic quadrilateral is equal to the interior opposite angle
(ext ∠, cyclic quad)

The angle where the radius meets the tangent is 90° (tgt ⊥ rad)