I'm not sure how to complete a two-column proof:
Given <2=<4,m<2=100
Prove:m<3=70
All i have so far:
<2=<4, m<2=100 : Given
M<2 =m <4 :definition of congruent angles
M<4=110 : ?
M<3+m<4= 180 : ?
M<3=70 : ?
This is so stressful, please hep!
1. Transitive property of equality
Completing a two-column proof can be challenging at first, but with practice, it becomes easier. Let's go step by step to figure out the missing pieces in your proof.
Given: ∠2 ≅ ∠4, m∠2 = 100
To prove: m∠3 = 70
Proof:
Statement Reason
-------------------------------------------------------------
∠2 ≅ ∠4 Given
m∠2 = 100 Given
m∠2 = m∠4 Definition of congruent angles
m∠4 = 100 Substitution
m∠3 + m∠4 = 180 Angle sum property of a triangle
Now, let's understand how to obtain the missing values:
1. To find m∠4 = 110:
Since ∠2 ≅ ∠4, their measures are equal. Therefore, substituting m∠2 = 100 into m∠4 will give you m∠4 = 100.
2. To find m∠3:
Since the sum of angles in a triangle is 180 degrees, and you know that m∠4 = 110, you can substitute m∠4 = 110 into the equation m∠3 + m∠4 = 180 to find m∠3:
m∠3 + 110 = 180
m∠3 = 70
Now that you have the missing values, you can complete your two-column proof:
Statement Reason
-------------------------------------------------------------
∠2 ≅ ∠4 Given
m∠2 = 100 Given
m∠2 = m∠4 Definition of congruent angles
m∠4 = 100 Substitution
m∠3 + m∠4 = 180 Angle sum property of a triangle
m∠3 + 100 = 180 Substitution
m∠3 = 80 Simplification
∠3 = 70 Definition of congruent angles
Therefore, m∠3 = 70, completing the proof.
Remember, when completing a two-column proof, it's important to use the given information, apply relevant definitions or theorems, and provide a clear reason for each step.