Practice Geometric Proofs in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
Geometric proofs establish that a geometric claim is true by chaining justified statements from definitions, theorems, and givens.
It is a legal argument where each line needs a valid reason.
Showing a random 20 of 50 problems.
Example 1
mediumWhat is a 'lemma' in mathematics?
Example 2
mediumGiven: and are vertical angles. Prove in two steps with reasons.
Example 3
mediumProve: The sum of the interior angles of a triangle is .
Example 4
easyWhat does CPCTC stand for, and when is it used?
Example 5
mediumIn a proof, you have and . What can you conclude and by what property?
Example 6
mediumWhy must each step in a proof have a justification?
Example 7
mediumDefine a 'biconditional' statement.
Example 8
easyWhich is a valid reason in a proof: 'it looks equal' or 'vertical angles are congruent'?
Example 9
mediumGiven and , prove where are arranged so is shared.
Example 10
easyWhich property justifies that a segment is congruent to itself?
Example 11
easyWhat is a 'given' in a geometric proof?
Example 12
mediumWhat distinguishes a 'flow proof' from a 'two-column proof'?
Example 13
mediumProve that the base angles of an isosceles triangle are equal.
Example 14
mediumProve: The diagonals of a parallelogram bisect each other.
Example 15
easyWhat is a theorem?
Example 16
challengeProve that in any triangle, the three perpendicular bisectors of the sides meet at a single point (the circumcenter).
Example 17
easyIn a proof, what is the 'prove' statement?
Example 18
easyWhat congruence shortcut is used when two triangles share three pairs of congruent corresponding sides?
Example 19
easyName the property used to justify '' in a proof.
Example 20
hardWhy is 'AAA' (three pairs of congruent angles) NOT a valid triangle congruence shortcut?