Angle facts, congruence, similarity and quadrilateral properties

A core WJEC reasoning topic. Most reasoning questions worth 4+ marks combine two or more of these facts.

Essential angle facts (must be quoted by name)

• Angles on a straight line sum to 180°.
• Angles around a point sum to 360°.
• Vertically opposite angles are equal.
• Angles in a triangle sum to 180°.
• Exterior angle of a triangle = sum of the two opposite interior angles.
• Angles in a quadrilateral sum to 360°.

Parallel-line rules

• Corresponding angles (F-shape) are equal.
• Alternate angles (Z-shape) are equal.
• Co-interior / allied angles (C-shape) sum to 180°.

WJEC requires the EXACT phrasing — "alternate angles are equal", not "Z angles".

Polygon angles

• Sum of interior angles of n-gon = (n − 2) × 180°.
• Sum of exterior angles of any polygon = 360°.
• Regular n-gon: each exterior = 360/n; each interior = 180 − (360/n).

Quadrilateral properties

Quad	Sides	Angles	Diagonals
Square	4 equal	All 90°	Equal, perpendicular, bisect
Rectangle	2 pairs equal	All 90°	Equal, bisect each other
Rhombus	4 equal	Opposite equal	Perpendicular, bisect angles
Parallelogram	Opposite equal	Opposite equal	Bisect each other (not equal)
Trapezium	One pair parallel	Co-interior pairs	—
Kite	2 pairs adjacent equal	One pair equal (between unequal sides)	Perpendicular; one bisects the other

Similarity vs congruence

• Congruent — same shape AND same size. All sides and angles equal.
• Similar — same shape, different size. Angles equal, sides in same ratio (scale factor).

To prove similarity, show all corresponding angles are equal (AA is enough — third angle follows).

Combining facts in a reasoning chain

WJEC mark scheme awards M1 for each fact correctly quoted with reason. Layout:

• Statement of angle = number° (reason).
• Next statement = number° (reason).
• Conclude.

WJEC exam tip

Every step must include a REASON in standard wording. "x = 50° because alternate angles are equal" gets the mark. "x = 50°" alone does not.