if you could just help me out with one, i would be blessed
1) Complete the proof.
Given: WX≅YZ
Prove: YZ≅WX
Statement Reason
1) WX≅YZ 1) ?
2) ? 2) Definition of Congruent Segments
3) YZ=WX 3) Symmetric Property of Congruence
4) YZ≅WX 4) ?
2) Complete the proof.
Given: m∠2=90, ∠1≅∠3
Angles 1 and 2 are adjacent, and angles 2 and 3 are adjacent. The three angles form a straight line.
Statement Reason
1) m∠2=90, ∠1≅∠3 1) Given
2) m∠3=m∠1 2) Definition of Congruent Angles
3) m∠1+m∠2+m∠3=180 3)?
4) m∠1+90+m∠1=180 4) ?
5) m∠1+m∠1=90 5) Subtraction Property of Equality
6) 2(m∠1)=90 6) Definition of Multiplication
7) m∠1=45 7) ?
Let's go through each of the proof statements and figure out the reasons for each step.
Proof 1:
1) WX≅YZ 1) Given - This is the given information in the problem.
2) ? 2) Definition of Congruent Segments - This step is missing the reason, but it should state that if two line segments are congruent, then they have equal length.
3) YZ=WX 3) Symmetric Property of Congruence - This step follows from the given information. If WX is congruent to YZ, then YZ is congruent to WX using the symmetric property of congruence.
4) YZ≅WX 4) ? - This step is missing the reason, but it should state that if two line segments have equal length, then they are congruent.
Proof 2:
1) m∠2=90, ∠1≅∠3 1) Given - This is the given information in the problem.
2) m∠3=m∠1 2) Definition of Congruent Angles - This step states that if two angles are congruent, then they have equal measure.
3) m∠1+m∠2+m∠3=180 3) ? - This step is missing the reason, but it should state that the sum of the measures of the angles in a straight line is 180 degrees.
4) m∠1+90+m∠1=180 4) ? - This step is missing the reason, but it should state that if an angle is a right angle (90 degrees), then the sum of its measure with the measures of the adjacent angles in a straight line is 180 degrees.
5) m∠1+m∠1=90 5) Subtraction Property of Equality - This step states that you can subtract the same quantity from both sides of an equation without changing the equality.
6) 2(m∠1)=90 6) Definition of Multiplication - This step states that you can multiply both sides of an equation by the same quantity without changing the equality.
7) m∠1=45 7) ? - This step is missing the reason, but it should state that dividing both sides of an equation by the same quantity gives us the value of the variable.
By filling in the missing reasons in steps 2, 3, 4, and 7, the proofs will be complete.
1) Complete the proof
Statement 1: WX ≅ YZ (Given)
Reason 2: Definition of Congruent Segments
Statement 3: YZ = WX (Symmetric Property of Congruence)
Reason 4: Definition of Congruent Segments
Therefore, YZ ≅ WX is proven.
2) Complete the proof
Statement 1: m∠2 = 90, ∠1 ≅ ∠3 (Given)
Reason 2: Definition of Congruent Angles
Statement 3: m∠1 + m∠2 + m∠3 = 180
Reason 4: Angle Sum Theorem (Angles 1, 2, and 3 form a straight line, so their measures add up to 180 degrees)
Statement 4: m∠1 + 90 + m∠1 = 180
Reason 5: Substitution Property of Equality
Statement 5: m∠1 + m∠1 = 90
Reason 6: Subtraction Property of Equality
Statement 6: 2(m∠1) = 90
Reason 7: Definition of Multiplication
Statement 7: m∠1 = 45
Reason 8: Division Property of Equality
Therefore, m∠1 = 45 is proven.