Geometric proof and deductive reasoning

What is deductive reasoning in a geometric proof?

Explain why measuring a diagram is not the same as proving a result.

State the SSS congruence test in words.

State the SAS congruence test in words.

If two parallel lines are cut by a transversal, what can be said about alternate interior angles?

What does it mean for two triangles to be similar?

In a proof, why should every statement have a reason?

Name one way to disprove a universal geometric claim.

If two triangles are congruent, what can be concluded about their corresponding sides and angles?

Give one example of a geometric fact that is often used as a reason in a proof.

Triangle ABC is isosceles with AB = AC. Draw a line from A to the midpoint of BC and use congruent triangles to prove that the base angles at B and C are equal.

Two triangles have AB = DE, BC = EF and angle ABC = angle DEF. Write a proof that the triangles are congruent, then state one pair of corresponding sides that must be equal.

Lines l and m are parallel. A transversal creates an angle of 72°. Find all adjacent and corresponding angle measures that follow, giving a reason for each step.

A student says, “The two triangles look the same size, so they are congruent.” Explain why this is not a proof and rewrite the argument using a valid congruence test.

Two triangles have angles 35°, 65° and 80°. Prove that they are similar, then find the side corresponding to 12 cm if the scale factor is 1.5.

Prove that the opposite angles formed by two intersecting straight lines are equal. Use straight-line angle facts and write your reasoning as a clear chain.

Create a counterexample to the claim: “Every quadrilateral with one pair of parallel sides is a parallelogram.” Explain why your example disproves the claim.

A quadrilateral has both pairs of opposite sides parallel. Use angle facts from parallel lines to prove that opposite angles are equal.

A dynamic geometry program suggests that a property is always true after many dragged examples. Explain what this evidence can and cannot show, then describe what a proof would still need.

Write a complete geometric proof problem of your own involving parallel lines, congruent triangles or similar triangles. Include a labelled diagram description, givens, proof steps and final conclusion.