I have no idea where to start! and I've got lots of these to write.
Directions say write a two-column proof...
Given: segment AB is congruent to segment XY, AC is is congruent to XZ, and BC is congruent to YZ.
Prove: triangle ABC is congruent to triangle XYZ
If three corresponding pairs of sides of two triangles are congruent, the triangles are congruent.
Sometimes that is called the side-side-side theorem. Put that in the right hand column. This looks like a one-step proof to me.
It has been a long time since I did two-column proofs
When starting a proof, it's important to understand what information is given and what you need to prove. In this case, you are given that certain segments are congruent, and you need to prove that two triangles are congruent. The fact that the proof is a two-column proof means that you will be organizing your statements and reasons in two separate columns.
Here's how you can approach this proof step-by-step:
Step 1: Start by writing out what is given:
Given: AB ≅ XY, AC ≅ XZ, BC ≅ YZ.
Step 2: To prove that two triangles are congruent, you typically use a congruence criterion. In this case, the given information is about segment congruence, so you can consider the Side-Side-Side (SSS) congruence criterion. Write that down as your first reason:
Reason 1: SSS congruence criterion.
Step 3: Next, you can state that the corresponding sides of the triangles are congruent based on the given information. Write down the corresponding sides:
Reason 2: Corresponding sides are congruent.
AB ≅ XY
AC ≅ XZ
BC ≅ YZ
Step 4: Now, you can write down the triangles you are working with. This step involves marking the vertices of the triangles and labeling them accordingly:
Reason 3: Triangles ABC and XYZ (Label the vertices as needed)
Step 5: State that the corresponding angles are congruent. This is a common step in most congruence proofs:
Reason 4: Corresponding angles are congruent (not specified in the given information).
Step 6: Lastly, indicate that Triangle ABC is congruent to Triangle XYZ using the SSS congruence criterion:
Reason 5: Triangles ABC and XYZ are congruent (by SSS criterion).
That's it! You have completed a two-column proof for this problem. Remember to organize your statements and reasons in two separate columns, with the statement on the left and the reason on the right.