Use the choices below to complete the proof.
Given: a⊥d , a⊥c
Prove: d∥c
(5 points)
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Statements Reasons
1 a⊥d , a⊥c
1. Response area
2. m<1 = 90 degrees; m<6 = 90 Degrees 2. Response area
3. m<1=m<6 3.Response area
4. < 1 and <6 are corresponding angles 4. Response area
5. d∥c
5. Response area
1 a⊥d , a⊥c
2. m<1 = 90 degrees; m<6 = 90 Degrees 2. Definition of perpendicular lines
3. m<1=m<6 3. Definition of congruent angles
4. < 1 and <6 are corresponding angles 4. Definition of corresponding angles
5. d∥c 5. Definition of parallel lines
Statements Reasons
1 a⊥d , a⊥c
1. Given
2. m<1 = 90 degrees; m<6 = 90 degrees
2. Definition of perpendicular lines
3. m<1 = m<6
3. Definition of congruent angles
4. <1 and <6 are corresponding angles
4. Corresponding angles congruence theorem
5. d∥c
5. Definition of parallel lines
To prove that d∥c, we can use the properties of perpendicular lines and angles.
Given: a⊥d, a⊥c
To prove: d∥c
Proof:
1. Given: a⊥d, a⊥c
2. m<1 = 90 degrees; m<6 = 90 Degrees (Reason: Definition of perpendicular lines)
3. m<1=m<6 (Reason: Angles formed by two perpendicular lines are congruent)
4. <1 and <6 are corresponding angles (Reason: Corresponding angles formed by two lines intersected by a transversal are congruent)
5. d∥c (Reason: If two angles are congruent and corresponding, then the lines they form are parallel)
By using the given information and applying the properties of perpendicular lines and angles, we have proven that d∥c.