Geometric Proofs Quiz
Questions: 16 · 10 minutes
1. A proof by contradiction begins by assuming that a proposed statement is false. What must the argument eventually derive to complete the proof?
A second example supporting the assumption
A diagram that appears inconsistent
A contradiction with a given fact, definition, or established theorem
The converse of the proposed statement
2. A student proves that a quadrilateral's diagonals are congruent and immediately concludes that the quadrilateral is a rectangle. Why is this conclusion invalid?
Rectangles never have congruent diagonals
Congruent diagonals alone are not sufficient to prove that a quadrilateral is a rectangle
A rectangle must have perpendicular diagonals, which was not shown
Congruent diagonals guarantee that a quadrilateral is a square instead
3. Triangles ABC and ADC share side AC. Which property justifies writing AC = AC while proving the triangles congruent?
Reflexive Property
Transitive Property
Symmetric Property
Substitution Property
4. In triangles JKL and MNO, angle J is congruent to angle M, side JK is congruent to side MN, and angle K is congruent to angle N. Which congruence theorem applies?
AAS
ASA
SAS
SSS
5. A proof states that triangle ABC is congruent to triangle DEF in that order. Which pair of sides corresponds correctly?
AB and EF
AC and EF
BC and DE
AC and DF
6. Ray BD bisects angle ABC. Which statement must be true?
Angle ABD and angle ABC are complementary
BD is perpendicular to AC
Angle ABD is congruent to angle DBC
Angle ABC and angle DBC are vertical angles
7. In triangles ABC and DEF, AB = DE, BC = EF, and angle B is congruent to angle E. Which theorem proves the triangles congruent?
SSS
ASA
AAS
SAS
8. Two lines intersect at point P. Which fact justifies that a pair of opposite angles at P are congruent?
Corresponding Angles Theorem
Vertical Angles Theorem
Linear Pair Postulate
Alternate Interior Angles Theorem
9. Point M is the midpoint of segment AB. Which statement follows directly from the definition of midpoint?
AM = MB
AM + MB = AM
M is perpendicular to AB
A and B are midpoints of AM and MB
10. Triangles PQR and XYZ are right triangles. Their hypotenuses PR and XZ are congruent, and legs PQ and XY are congruent. Which theorem proves the triangles congruent?
Side-Side-Angle
Angle-Angle
Hypotenuse-Leg
Pythagorean Theorem
11. A proof states that AB = CD and CD = EF. Which property justifies the conclusion AB = EF?
Transitive Property of Equality
Symmetric Property of Equality
Reflexive Property of Equality
Addition Property of Equality
12. A transversal crosses lines l and m, creating a congruent pair of alternate interior angles. Which result allows you to conclude that l is parallel to m?
The Alternate Interior Angles Theorem
The Perpendicular Transversal Theorem
The Vertical Angles Theorem
The Converse of the Alternate Interior Angles Theorem
13. Parallel lines r and s are cut by a transversal. Two interior angles lie on the same side of the transversal. What relationship should a proof establish between their measures?
Their measures are equal because they are vertical angles
Their measures have a difference of 90 degrees
Their measures add to 180 degrees
Their measures are each necessarily 90 degrees
14. Two triangles have two pairs of congruent corresponding angles. Which criterion is sufficient to prove that the triangles are similar?
SSS Congruence
SAS Congruence
HL Congruence
AA Similarity
15. A student knows that AB = DE, BC = EF, and angle A is congruent to angle D. What can the student conclude about triangles ABC and DEF from this information alone?
Congruence cannot be established because the information forms SSA
They are congruent by ASA
They are congruent by SSS
They are congruent by SAS
16. A proof has established that triangle ABC is congruent to triangle DEF. What principle can then justify that angle C is congruent to angle F?
Converse of the Pythagorean Theorem
Corresponding Parts of Congruent Triangles Are Congruent
Triangle Sum Theorem
Segment Addition Postulate