Statements Reasons
1. <1 and <2 are complementary 1. Given
2. m<1 +m<2 = 2.
3. <1 <4 3. Given
4. m<1 = m<4 4. Definition of congruence
5. <2 <3 5.
6. m<2 = m<3 6. Definition of congruence
7. m<4 + m<3 = 7.
8. <3 and <4 are complementary 8. Definition of Complementary Angles
7. m<4 + m<3 = 7. - This statement seems to be incomplete or incorrect.
Statement 5 and Statement 6 are missing reasons.
To prove that <3 and <4 are complementary angles, we can use the given statements and reasons provided:
Statements Reasons
1. <1 and <2 are complementary 1. Given
2. m<1 + m<2 = 2 2. Given
3. <1 < 4 3. Given
4. m<1 = m<4 4. Definition of congruence
5. <2 < 3 5. Given
6. m<2 = m<3 6. Definition of congruence
7. m<4 + m<3 = 7 7. Given
8. <3 and <4 are complementary 8. Definition of Complementary Angles
Now let's explain how we got to each statement and reason:
1. The given statement tells us that <1 and <2 are complementary angles. By definition, complementary angles add up to 90 degrees.
2. The given statement tells us that m<1 + m<2 equals 2. This means that the measures of <1 and <2 add up to 2.
3. The given statement tells us that <1 is less than <4. This indicates that <1 is smaller than <4 in terms of their degrees.
4. This statement comes from the definition of congruence. It states that if <1 and <4 are congruent, then their measures are equal.
5. The given statement tells us that <2 is less than <3. Similar to statement 3, this indicates that <2 is smaller than <3 in terms of their degrees.
6. This statement comes from the definition of congruence. It states that if <2 and <3 are congruent, then their measures are equal.
7. The given statement tells us that m<4 + m<3 equals 7. This means that the measures of <4 and <3 add up to 7.
8. According to the definition of complementary angles, angles that add up to 90 degrees are considered complementary angles. Since <3 and <4 add up to 7, which is less than 90 degrees, we can conclude that they are complementary angles.
Therefore, we have proven that <3 and <4 are complementary angles based on the given information and logical reasoning.