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) ?
1) Complete the proof:
Statement Reason
1) WX≅YZ 1) Given
2) XY=YZ 2) Definition of Congruent Segments
3) YZ=WX 3) Symmetric Property of Equality
4) YZ≅WX 4) Definition of Congruent Segments
2) Complete the proof:
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) Angle Sum Property of a Triangle
4) m∠1+90+m∠1=180 4) Substitution
5) 2m∠1+90=180 5) Combining like terms
6) 2m∠1=90 6) Subtraction Property of Equality
7) m∠1=45 7) Division Property of Equality
Sure, I can help you with these proofs. Let's go step by step through each statement and reason.
1) Given: WX≅YZ
To prove: YZ≅WX
Statement Reason
1) WX≅YZ Given
2) YZ≅WX Definition of Congruent Segments (if WX is congruent to YZ, then YZ is congruent to WX)
3) YZ=WX Symmetric Property of Congruence (if WX equals YZ, then YZ equals WX)
4) YZ≅WX Definition of Congruent Segments (if YZ equals WX, then YZ is congruent to WX)
2) Given: m∠2=90, ∠1≅∠3
Statement Reason
1) m∠2=90, ∠1≅∠3 Given
2) m∠3=m∠1 Definition of Congruent Angles (if ∠1 is congruent to ∠3, then ∠3 is congruent to ∠1)
3) m∠1+m∠2+m∠3=180 The three angles form a straight line (Angles on a straight line sum up to 180 degrees)
4) m∠1+90+m∠1=180 Substitution property (substituting m∠2 as 90°)
5) m∠1+m∠1=90 Subtraction Property of Equality (subtracting 90° from both sides)
6) 2(m∠1)=90 Simplification (combining like terms)
7) m∠1=45 Division Property of Equality (dividing both sides by 2)
I hope this helps! Let me know if you have any further questions.