STATEMENTS REASONS
I need help with reasoning for 3,4 and 5
1. ∠2 ≅ ∠4 1. Given
2. m∠2 = m∠4 2. Definition of Congruent Angles
3. m∠1+m∠2 = 180° ; m∠3+m∠4 = 180°-
4. m∠1 + m∠2 = m∠3 + m∠4-
5. m∠1 + m∠2 = m∠3 + m∠2-
6. m∠1 = m∠3 6. Subtraction Property of Equality
7. ∠1 ≅ ∠3 7. Definition of Congruent Angles
Sure, let me try to help you with reasoning for statements 3, 4, and 5 using humor:
3. m∠1 + m∠2 = 180°; m∠3 + m∠4 = 180°
Reasoning: Well, when it comes to angles, they like to add up to create a full circle of 360 degrees. But here, it seems like we only have half a circle, so the sum of m∠1 and m∠2 is equal to the sum of m∠3 and m∠4, which is like balancing out the missing half of the circle. It's like one big puzzle where all the pieces fit perfectly.
4. m∠1 + m∠2 = m∠3 + m∠4
Reasoning: Ah, it seems like the angles are having a competition here. They're trying to prove that their sums are equal on both sides. It's like a friendly game of "Guess the Sum" where each group of angles is determined to come up with the same answer. So, they all put their numbers together, and voila! The sums are magically equal.
5. m∠1 + m∠2 = m∠3 + m∠2
Reasoning: Oh, this statement is having a little identity crisis, isn't it? It seems like m∠2 is trying to be on both sides of the equation, as if it's lost and doesn't know where it truly belongs. It's like a fickle angle that just wants to be part of multiple equations. But hey, in the end, the equation still balances out, so maybe m∠2 is just exploring its options.
I hope that brings a smile to your face while understanding the reasoning behind these statements!
For reasoning statements 3, 4, and 5:
3. m∠1 + m∠2 = 180° ; m∠3 + m∠4 = 180°
- This statement is based on the Angle Sum Theorem, which states that the sum of the measures of the angles in any triangle is 180°.
4. m∠1 + m∠2 = m∠3 + m∠4
- This statement is an application of the Transitive Property of Equality, which states that if two quantities are both equal to a third quantity, then they are equal to each other.
5. m∠1 + m∠2 = m∠3 + m∠2
- This statement is a result of combining like terms. The measure of ∠2 on both sides of the equation is canceled out, leaving us with m∠1 = m∠3.
Therefore, in statement 6, we can conclude that m∠1 = m∠3.
Finally, in statement 7, we use the Definition of Congruent Angles to state that ∠1 ≅ ∠3, since they have equal measures.
I hope this helps! Let me know if you have any further questions.
To provide reasoning for statements 3, 4, and 5, we will analyze the given information and apply relevant mathematical properties:
3. m∠1 + m∠2 = 180° ; m∠3 + m∠4 = 180°
This statement follows from the fact that the sum of the measures of two angles forming a straight line is always 180 degrees.
4. m∠1 + m∠2 = m∠3 + m∠4
Statement 3 can be rewritten as "m∠1 + m∠2 = 180°" and "m∠3 + m∠4 = 180°". By substituting these values into statement 4, we get the result.
5. m∠1 + m∠2 = m∠3 + m∠2
This statement is incorrect. It seems to be an error in substituting the values wrongly. Since ∠2 is congruent to ∠4 (as given in statement 1), we can say m∠2 = m∠4. Therefore, the correct equation would be m∠1 + m∠2 = m∠3 + m∠4.
By using statement 4, we can substitute m∠1 + m∠2 = m∠3 + m∠4 into statement 7 to conclude:
m∠1 + m∠2 = m∠3 + m∠4
∠1 ≅ ∠3.
Therefore, statement 7 is valid based on the information provided.