Pass Check: Geometric Proof
Every proof step needs a named geometric reason - never state a fact without justifying it.
Proof
A logical chain of statements, each justified by a geometric fact, that shows a result must be true.
Alternate angles
Equal angles on opposite sides of a transversal crossing parallel lines, forming a Z shape.
Corresponding angles
Equal angles in matching positions where a transversal crosses parallel lines, forming an F shape.
Co-interior (allied) angles
Angles between parallel lines on the same side of a transversal, summing to 180 degrees, forming a C or U shape.
Quick check
Mixed quiz
1. Two triangles share a common angle and have two pairs of corresponding sides in the same ratio. What can you conclude, and by which reasoning?
2. Triangle ABC has a right angle at B. Triangle DEF has a right angle at E. AC=DF (hypotenuses equal) and AB=DE. Which condition proves congruence?
3. Triangle ABC and triangle DEF have AB=DE, angle A=angle D, angle B=angle E. Which condition proves congruence?
4. Two triangles have all three corresponding angles equal but different side lengths. Are they congruent or similar?
5. 5 workers can complete a job in 13 days. How many days would 10 workers take, assuming the same rate?
6. 6 workers can complete a job in 17 days. How many days would 12 workers take, assuming the same rate?
7. Is doubling the number of workers on a job (same rate) an example of direct or inverse proportion for time taken?
8. A 750ml bottle costs £4.50 and a 1.5 litre bottle costs £8.40. Which is better value per litre?