Angle facts, congruence, similarity, quadrilaterals

This is one of the most heavily examined Edexcel reasoning blocks. Higher Paper 1H or 2H typically has a 4–5 mark "find angle x" question that combines two or three of these facts in sequence.

Core angle facts (memorise the wording — Edexcel demands exact phrasing for the C1 reason)

• Angles on a straight line sum to 180°.
• Angles at a point sum to 360°.
• Vertically opposite angles are equal.
• Angles in a triangle sum to 180°.
• Angles in a quadrilateral sum to 360°.
• Exterior angle of a triangle equals the sum of the two interior opposite angles.
• Base angles of an isosceles triangle are equal.

Parallel-line facts (must use exact names)

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

Quadrilateral properties

Shape	Sides	Angles	Diagonals
Square	4 equal	4 right	Equal, perpendicular, bisect
Rectangle	Opp. equal	4 right	Equal, bisect
Rhombus	4 equal	Opp. equal	Perpendicular, bisect
Parallelogram	Opp. equal	Opp. equal	Bisect each other
Trapezium	One pair parallel	—	—
Kite	Two adjacent pairs equal	One pair equal	Perpendicular

Congruent triangles — four conditions

• SSS — three sides equal.
• SAS — two sides and the included angle equal.
• ASA / AAS — two angles and a corresponding side.
• RHS — right angle, hypotenuse, and one other side.

A correct congruence proof states the condition (SSS/SAS/etc.) and pairs the elements explicitly.

Similar triangles

Triangles are similar if all three angles are equal AAA — equivalent to "the sides are in the same ratio". Higher questions ask for the scale factor k; corresponding sides scale by k, areas by k², volumes by k³.

Common Edexcel exam tip

Every angle answer on Edexcel reasoning questions needs a numerical value AND a reason. Writing "70°" alone scores B1; writing "70° (alternate angles equal)" scores B1 + C1 — typically twice as many marks.