Write a two column proof.
Given: angle STV is congruent to angle TVU, angle STU is congruent to angle UVS.
Prove: Angle SVT is congruent to angle UTV.
What is the answer
To write a two-column proof for this problem, we need to list the statements and their corresponding reasons.
Statement | Reason
---------|----------
1. angle STV is congruent to angle TVU | Given
2. angle STU is congruent to angle UVS | Given
3. angle STV + angle STU = angle TVU + angle UVS | Angle Addition Postulate
4. angle SVT = angle STV + angle STU | Definition of angle SVT
5. angle UTV = angle TVU + angle UVS | Definition of angle UTV
6. angle SVT = angle UTV | Substitution Property of Equality
Let's explain the reasoning behind each statement:
1. The congruence of angle STV and angle TVU is given in the problem statement.
2. The congruence of angle STU and angle UVS is also given.
3. According to the Angle Addition Postulate, the sum of two angles is equal to the sum of their parts.
4. Using the definition of angle SVT, we can say that angle SVT is equal to the sum of angles STV and STU.
5. Similarly, using the definition of angle UTV, we can say that angle UTV is equal to the sum of angles TVU and UVS.
6. Using the substitution property of equality, we can substitute the values from statements 1, 2, and 3 into statements 4 and 5. This shows that angle SVT is congruent to angle UTV.
Therefore, we have proven that Angle SVT is congruent to angle UTV.