If x is the midpoint of line vy and wz
And the prove is triangle vwx is congruent triangle yzx can you help me solve this using two column prove
Sure! To prove that triangle VWX is congruent to triangle YZX using a two-column proof, we need to show that their corresponding sides and angles are congruent. Here's how you can go about solving it:
Step 1: Write down the given information in the left column of the proof.
Given: X is the midpoint of line VY and WZ.
Step 2: Write down statements and reasons for each step of the proof in the right column.
Statement | Reason
-----------------------------------------------
1. X is the midpoint of VY, WZ | Given
2. VX = XY, XW = XZ | Definition of Midpoint
3. VY = XZ | Substitution Property
4. ∠XVW = ∠YXZ | Vertical Angles Theorem
5. WX = YZ | Substitution Property
6. ∆VWX ≅ ∆YZX | SAS (Side-Angle-Side) congruence theorem
Step 3: Explain each step of the proof in words.
1. X is the midpoint of VY and WZ is given information.
2. By definition of a midpoint, VX is equal to XY (since X is the midpoint of VY) and XW is equal to XZ (since X is the midpoint of WZ).
3. By substitution, we can replace VY with XZ, as they are equal (according to the given information in step 1).
4. ∠XVW and ∠YXZ are vertical angles, and vertical angles are always congruent.
5. By substitution, we can replace WX with YZ, as they are equal (according to the given information in step 1).
6. All corresponding angles and sides of triangles VWX and YZX are congruent, so by SAS (side-angle-side) congruence theorem, we can conclude that ∆VWX is congruent to ∆YZX.
Step 4: Write the final statement/conclusion of the proof.
Therefore, triangle VWX is congruent to triangle YZX.
And that's how you can prove the congruence of triangles VWX and YZX using a two-column proof!