Question

The proof refers to the figure shown here. Drag the word choices below to supply the missing reasons in the proof. Lines X, V, and W intersect at point Z. Angles W Z X and W Z V are marked, but no measures are given. Substitution Congruent Supplements Theorem Law of Syllogism Linear Pairs Theorem of Angle Addition Postulate: Definition of Perpendicular Lines Definition of Linear Pair Vertical Angles The Transitive Property of Equality

Statement Reason
1 ∠WZX ≅ ∠WZV Given
2 ∠WZX and ∠WZV are a linear pair. _________
3 m∠WZX + m∠WZV = 180_________
4 m∠WZX + m∠WZX = 180_________
5 m∠WZX = 90 Subtraction Property of Equality
6 WY ⊥ VX __________

Answer 1

Reason 1: ∠WZX ≅ ∠WZV (Given)

Reason 2: ∠WZX and ∠WZV are a linear pair (Definition of Linear Pair)

Reason 3: m∠WZX + m∠WZV = 180 (Linear Pairs Theorem)

Reason 4: m∠WZX + m∠WZX = 180 (Substitution)

Reason 5: m∠WZX = 90 (Subtraction Property of Equality)

Reason 6: WY ⊥ VX (Definition of Perpendicular Lines)

Step-by-step explanation:

The proof provided approaches a geometry problem usually covered in high school mathematics courses. It demonstrates the use of geometric postulates and theorems to establish relationships between angles and lines in a given figure.

Statement 2 uses the Definition of Linear Pair to explain why ∠WZX and ∠WZV form a linear pair.

Statement 3 applies the Linear Pairs Theorem or Congruent Supplements Theorem to show that these angles add up to 180°.

Statement 4 applies the Substitution property to establish that adding the measure of ∠WZX to itself equals 180°.

Statement 5 utilizes the Subtraction Property of Equality to deduce that ∠WZX is a right angle, and hence measures 90°.

Statement 6 applies the Definition of Perpendicular Lines to indicate that line WY is perpendicular to VX, concluding the proof.