Geometrical Proof Flashcards

All 6 cards in this deck

What is the standard reason quoted for the two angles opposite the equal sides of an isosceles triangle being equal?

Base angles of an isosceles triangle are equal.

State two properties of a parallelogram used in geometrical proofs.

Opposite sides are equal and parallel; opposite angles are equal.

Which two angle reasons can you quote for equal angles when a line crosses a pair of parallel lines?

Alternate angles are equal; corresponding angles are equal. (Co-interior angles sum to $180^\circ$.)

What are the steps to build a chain of reasoning for a proof?

e.g. prove the exterior angle $x$ of a triangle equals the sum of the two opposite interior angles $a$ and $b$

1. Write a fact with its reason: $x = 180^\circ - c$ (angles on a straight line).
2. Write the next fact with its reason: $a + b = 180^\circ - c$ (angles in a triangle sum to $180^\circ$).
3. Link them to the required conclusion: $x = a + b$.

True or false? Measuring the angles on an accurate diagram is enough to prove a geometrical result.

False. A proof must use known geometric facts, each with a reason, so it holds in every case.

True or false? The fact that the base angles of an isosceles triangle are equal can be proved using congruent triangles.

True. Splitting the triangle along its line of symmetry gives two congruent triangles (SSS or SAS), so the base angles are equal.