Statements Reasons 1. <1 and <2 are complementary 1. Given 2. m<1 +m<2 = 90° 2. Response area 3. <1≅ <4 3. Given 4. m<1 = m<4 4. Definition of congruence 5. <2 ≅ <3 5. Response area 6. m<2 = m<3 6. Definition of congruence 7. m<4 + m<3 = 90° 7. Response area 8. <3 and <4 are complementary 8. Definition of Complementary Angles
(Given)(Definition of Complementary Angles)(Vertical Angles Theorem)(Substitution)(Definition of Supplementary Angles)(Definition of a linear pair)
The given statements and reasons form a valid argument:
1. <1 and <2 are complementary (Given)
2. m<1 + m<2 = 90° (Given)
3. <1 ≅ <4 (Given)
4. m<1 = m<4 (Definition of congruence)
5. <2 ≅ <3 (Response area)
6. m<2 = m<3 (Definition of congruence)
7. m<4 + m<3 = 90° (Response area)
8. <3 and <4 are complementary (Definition of Complementary Angles)
The reasons given support the statements made, and the logical progression of the arguments leads to the conclusion that <3 and <4 are complementary angles.
please fill out the blank area questions with the following(Given)(Definition of Complementary Angles)(Vertical Angles Theorem)(Substitution)(Definition of Supplementary Angles)(Definition of a linear pair)
1. <1 and <2 are complementary (Given)
2. m<1 + m<2 = 90° (Given)
Response area
3. <1≅ <4 (Given)
4. m<1 = m<4 (Definition of congruence)
Response area
5. <2 ≅ <3 (Response area)
6. m<2 = m<3 (Definition of congruence)
Response area
7. m<4 + m<3 = 90° (Response area)
8. <3 and <4 are complementary (Definition of Complementary Angles)
Response area
Given
Definition of Complementary Angles
Vertical Angles Theorem
Substitution
Definition of Supplementary Angles
Definition of a linear pair
Question Complete the following paragraph proof. (You may use the choices more than once and you may not use all the choices) Given: <5 and <7 are supplementary. <7 and <9 are also supplementary Prove: <5 ≅ <9 (5 points)We know that <5 and <7 are supplementary. <7 and <9 are also supplementary because it is Response area<5 + m<7 = Response area and m< 7 + m<9 = Response area, by definition of supplementary angles. Then, m<5 + m<7 = m<7 + m<9 by the Response area. Subtract m<7 from each side and you get m<5 = m<9. Then by the definition of congruence, <5 ≅ Response area
Given: <5 and <7 are supplementary. <7 and <9 are also supplementary.
Prove: <5 ≅ <9
Proof:
1. <5 and <7 are supplementary (Given)
2. <7 and <9 are supplementary (Given)
3. <5 + <7 = 180° (Definition of supplementary angles)
4. <7 + <9 = 180° (Definition of supplementary angles)
5. <5 + <7 = <7 + <9 (Substitution)
6. Subtract <7 from each side: <5 = <9 (Subtraction Property of Equality)
7. <5 ≅ <9 (Definition of congruence)
Therefore, we have proved that <5 ≅ <9 using the given information and the definition of congruence.
Justify each step in the proof below (You may use a choice more than once. You will not use all the choices given. ) EG = 68Given : EG = 68 Prove: x = 8 1. EG = 68, EF = 8x-12, FG = 2x 1. Given2. EF + FG = EG 2. Response area 3. 8x - 12 + 2x = 68 3. Response area 4. 10x - 12 = 68 4. Response area 5. 10x = 80 5. Response area 6. x = 8 6. Response area
Justification for each step in the proof:
1. EG = 68, EF = 8x-12, FG = 2x (Given)
- Given information is stated.
2. EF + FG = EG
- The sum of the two sides of a triangle must be greater than the third side (Triangle inequality theorem).
3. 8x - 12 + 2x = 68
- Substitution of the given values into the equation.
4. 10x - 12 = 68
- Simplification of the left side of the equation.
5. 10x = 80
- Addition of 12 to both sides of the equation.
6. x = 8
- Division of both sides of the equation by 10.
Each step in the proof follows logically from the properties of equality and the given information.