Math Problem Statement

Prove that XY is congruent to XZ given that X is the midpoint of WY and WX is congruent to XZ.

Solution

Let's complete the proof shown in the image step by step. The goal is to prove that XY‾≅XZ‾\overline{XY} \cong \overline{XZ}.

Given:

  • XX is the midpoint of WY‾\overline{WY},
  • WX‾≅XZ‾\overline{WX} \cong \overline{XZ}.

Proof:

StatementsReasons
1. XX is the midpoint of WY‾\overline{WY}1. Given
2. WX=XYWX = XY2. Definition of midpoint
3. WX‾≅XZ‾\overline{WX} \cong \overline{XZ}3. Given
4. WX=XZWX = XZ4. Definition of congruent segments
5. XY=XZXY = XZ5. Transitive property of equality
6. XY‾≅XZ‾\overline{XY} \cong \overline{XZ}6. Definition of congruent segments

This table completes the two-column proof.

Would you like more detailed explanations or have any questions on these steps? Here are some related questions to explore this further:

  1. What is the definition of a midpoint in geometry?
  2. How does the transitive property of equality work in geometry proofs?
  3. Can you explain why XY‾≅XZ‾\overline{XY} \cong \overline{XZ} implies equal lengths?
  4. What role do congruent segments play in geometric proofs?
  5. How would this proof change if XX were not the midpoint?

Tip: Always double-check your reasoning and definitions, as they provide the foundation for all proofs!

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Math Problem Analysis

Mathematical Concepts

Geometry
Congruence
Midpoint

Formulas

-

Theorems

Definition of midpoint
Definition of congruent segments
Transitive property of equality

Suitable Grade Level

Grades 9-10

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