Geometry Quiz

Which of the following illustrates the Law of Syllogism?

• [(p → q) v (q ( r) ] → (p → r)

• [(p → q) ^ (q → r) ] → (p → r)

• [(p → q) ^ q ] → p

• [(p → q) ^ p ] → q

Answer explanation

The Law of Syllogism states that if p implies q and q implies r, then p implies r. The correct choice, [(p → q) ^ (q → r)] → (p → r), directly illustrates this principle.

Which of the following illustrates the Law of Detachment?

• [(p → q) v (q ( r) ] → (p → r)

• [(p → q) ^ (q → r) ] → (p → r)

• [(p → q) ^ q ] → p

• [(p → q) ^ p ] → q

Answer explanation

The Law of Detachment states that if 'p → q' is true and 'p' is true, then 'q' must also be true. The correct choice '[(p → q) ^ p] → q' directly applies this principle, confirming 'q' when both conditions are met.

Which best describes the statement "A plane contains at least 3 points not on the same line"?

• Always true

• Sometimes true

• Never true

• Cannot tell

Answer explanation

The statement "A plane contains at least 3 points not on the same line" is always true because, by definition, a plane is a flat surface that extends infinitely and requires at least three non-collinear points to define it.

Which is a type of proof where you write a paragraph to explain why a conjecture for a given situation is true?

• Argument

• Explanation

• Paragraph proof

• Two-column proof

Answer explanation

A paragraph proof is a type of proof that presents a logical argument in a written paragraph format, explaining why a conjecture is true. This distinguishes it from other proof types like two-column proofs.

If 3x = 6, then x = 2. Choose the property that justifies the statement.

• Addition

• Subtraction

• Square root

• Division

Answer explanation

To solve for x in the equation 3x = 6, we divide both sides by 3. This operation isolates x, leading to x = 2. Thus, the property that justifies this step is Division.

If m∠A = 10 and m∠B = 10, then m∠A = m∠B. Choose the property that justifies the statement.

• Reflexive

• Symmetric

• Substitution

• Equality

Answer explanation

The statement m∠A = m∠B is justified by the Symmetric Property, which states that if a = b, then b = a. Here, since both angles are equal to 10, it confirms that m∠A = m∠B.

If PS ≅ WX, then PS = WX. Choose the property that justifies the statement.

• Reflexive

• Symmetric

• Definition of congruent segments

• Transitive

Answer explanation

The statement PS ≅ WX means that PS and WX are congruent segments. By the definition of congruent segments, if two segments are congruent, their lengths are equal, thus PS = WX. This justifies the statement.

If A, B, and N are collinear and AB + BN = AN, which point is between the other two points?

• A

• B

• N

• Cannot tell

Answer explanation

Since AB + BN = AN, point B must be between A and N. If B were not between them, the distances would not add up correctly. Therefore, B is the point that lies between A and N.

Find the value of x if the equation is 55° = (x + 30)°.

• 25

• 35

• 55

• 125

Answer explanation

To find x, rearrange the equation: 55° = (x + 30)°. Subtract 30° from both sides: 55° - 30° = x, which simplifies to x = 25°. Thus, the correct answer is 25.

If m∠ABD = 56, find m∠DBC.

• 124

• 56

• 44

• 34

Answer explanation

Since m∠ABD = 56°, and angles on a straight line sum to 180°, we have m∠DBC = 180° - 56° = 124°. However, if we consider the triangle formed, m∠DBC = 180° - 56° - 90° = 34°, making the correct answer 34.