Question
The steps of the proof are shown.
GIVEN ⇒ 2AB = AC
PROVE: AB = BC
1. 2AB = AC (Given)
2. AB + AB = AC (____)
3. AB + BC = AC (Segment Addition Postulate)
4. AB + AB = AB + BC (____)
5. AB = BC (Subtraction Property)
What is the reason for step 2?
- Given
- Distributive Property
- Substitution Property
- Transitive Property
Hint:
In this question . we have given a line A following B and C. And given is 2AB = AC and we have to prove here AB = AC. Now have to find the step 2 reason. Use property of equality.
The correct answer is: Distributive Property
Here, we have to find the steps 2 reason.
Firstly, given a line A following B and C and 2AB = AC .
Now ,
1. 2AB = AC
2. AB + AB = AC ( Distributive property)
3. AB + BC = AC (Segment Addition Postulate)
4. AB + AB = AB + BC (Substitution property )
5. AB = BC ( subtraction property)
Therefore , the reason of step 2 is distributive property.
The correct answer is Distributive property
Or,
Distributive Property
The whole proof:
2AB = AC (Given)
AB + AB = AC (Distributive Property)
AB + BC = AC (Segment Addition Postulate)
AB + AB = AB + BC (Substitution Property)
AB = BC (Subtraction Property)
Distributive Property: A crucial mathematical property that will help you solve many algebraic problems is the distributive property.
The distributive property, also used as the distributive property of multiplication, demonstrates how to solve particular algebraic statements that combine addition and multiplication. For example, a number multiplied by a sum has the same effect as doing each multiplication separately, according to the literal definition of the distributive property.
The distributive property appears in an equation: a(b+c)=ab+ac. The substitution property of equality, if two variables are equal, x and y, respectively, then x can be used in place of y in any equation or expression, and 'y' can is used in place of x.
Related Questions to study
Give the reason for statement #4.
Given: PS = RT, PQ = ST
Prove: QS = RS
| Statement | Reason |
| 1. PS = RT, PQ = ST |
1. |
| 2. PQ + QS = PS |
2. |
| 3. ST + QS = RT |
3. |
| 4. RS + ST = RT |
4. |
| 5. ST + QS = RS + ST |
5. |
| 6. QS = RS |
6. |
Geometrically, a line segment with three collinear points is subject to the segment addition postulate. By the segment addition postulate, point B will only be on the same line segment as points A and C if the sum of AB and BC equals AC if there are two given points on the segment between them, A and C. According to the segment addition postulate, if a line segment has endpoints A and C, and a third point B, then only if the equation AB + BC = AC is true does the third point B lie on the line segment AC. To further comprehend this postulate, look at the illustration provided below.
Give the reason for statement #4.
Given: PS = RT, PQ = ST
Prove: QS = RS
| Statement | Reason |
| 1. PS = RT, PQ = ST |
1. |
| 2. PQ + QS = PS |
2. |
| 3. ST + QS = RT |
3. |
| 4. RS + ST = RT |
4. |
| 5. ST + QS = RS + ST |
5. |
| 6. QS = RS |
6. |
Geometrically, a line segment with three collinear points is subject to the segment addition postulate. By the segment addition postulate, point B will only be on the same line segment as points A and C if the sum of AB and BC equals AC if there are two given points on the segment between them, A and C. According to the segment addition postulate, if a line segment has endpoints A and C, and a third point B, then only if the equation AB + BC = AC is true does the third point B lie on the line segment AC. To further comprehend this postulate, look at the illustration provided below.
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Find the measure of each angle in the diagram.
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Two lines that are not perpendicular intersect such that ∠1 and ∠2 are a linear pair, ∠1 and ∠4 are a linear pair, and ∠1 and ∠3 are vertical angles. Tell whether the following statement is true or false.
Two angles are said to be supplementary is the sum of their measures is 180°.
Two lines that are not perpendicular intersect such that ∠1 and ∠2 are a linear pair, ∠1 and ∠4 are a linear pair, and ∠1 and ∠3 are vertical angles. Tell whether the following statement is true or false.
Two angles are said to be supplementary is the sum of their measures is 180°.
Two lines that are not perpendicular intersect such that ∠1 and ∠2 are a linear pair, ∠1 and ∠4 are a linear pair, and ∠1 and ∠3 are vertical angles. Tell whether the following statement is true or false.
Vertical angles are always equal.
Two lines that are not perpendicular intersect such that ∠1 and ∠2 are a linear pair, ∠1 and ∠4 are a linear pair, and ∠1 and ∠3 are vertical angles. Tell whether the following statement is true or false.
Vertical angles are always equal.
Two lines that are not perpendicular intersect such that ∠1 and ∠2 are a linear pair, ∠1 and ∠4 are a linear pair, and ∠1 and ∠3 are vertical angles. Tell whether the following statement is true or false.
The sum of the angles of a linear pair is 180°.
Two lines that are not perpendicular intersect such that ∠1 and ∠2 are a linear pair, ∠1 and ∠4 are a linear pair, and ∠1 and ∠3 are vertical angles. Tell whether the following statement is true or false.
The sum of the angles of a linear pair is 180°.
Two lines that are not perpendicular intersect such that ∠1 and ∠2 are a linear pair, ∠1 and ∠4 are a linear pair, and ∠1 and ∠3 are vertical angles. Tell whether the following statement is true or false.
The sum of the angles of linear pair is 180°.
Two lines that are not perpendicular intersect such that ∠1 and ∠2 are a linear pair, ∠1 and ∠4 are a linear pair, and ∠1 and ∠3 are vertical angles. Tell whether the following statement is true or false.
The sum of the angles of linear pair is 180°.
Two lines that are not perpendicular intersect such that ∠1 and ∠2 are a linear pair, ∠1 and ∠4 are a linear pair, and ∠1 and ∠3 are vertical angles. Tell whether the following statement is true or false.
Vertical angles are always equal.
Two lines that are not perpendicular intersect such that ∠1 and ∠2 are a linear pair, ∠1 and ∠4 are a linear pair, and ∠1 and ∠3 are vertical angles. Tell whether the following statement is true or false.
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Two lines that are not perpendicular intersect such that ∠1 and ∠2 are a linear pair, ∠1 and ∠4 are a linear pair, and ∠1 and ∠3 are vertical angles. Tell whether the following statement is true or false.
Here, sum of angles 1 and 2 is 180°.
Two lines that are not perpendicular intersect such that ∠1 and ∠2 are a linear pair, ∠1 and ∠4 are a linear pair, and ∠1 and ∠3 are vertical angles. Tell whether the following statement is true or false.
Here, sum of angles 1 and 2 is 180°.
Which property does the statement illustrate?
Same applies on number and shapes.
Which property does the statement illustrate?
Same applies on number and shapes.
Which property does the statement illustrate?
If a=b, then b = a.
Which property does the statement illustrate?
If a=b, then b = a.
Find the measure of each angle in the diagram.
Find the measure of each angle in the diagram.
Complete the statement with <, >, or =.
If m∠ 4 = 30, then m∠ 5? m∠ 4.
When two angles are formed on a straight line, they are called linear pair.
Complete the statement with <, >, or =.
If m∠ 4 = 30, then m∠ 5? m∠ 4.
When two angles are formed on a straight line, they are called linear pair.
Complete the statement with <, >, or =.
m∠ 8 + m∠ 6? 150
When two angles are formed on a straight line, they are called linear pair.
Complete the statement with <, >, or =.
m∠ 8 + m∠ 6? 150
When two angles are formed on a straight line, they are called linear pair.
What is the reason for statement 2?
| Statement | Reason | |
| 1 |  |
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| 2 |  |
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| 3 |  |
Alternate exterior angles are always equal.
What is the reason for statement 2?
| Statement | Reason | |
| 1 | |
|
| 2 | |
|
| 3 | |
Alternate exterior angles are always equal.
What is the reason for statement 3?
| Statement | Reason | |
| 1 | |
|
| 2 | |
|
| 3 | |
Corresponding angles are equal.
What is the reason for statement 3?
| Statement | Reason | |
| 1 | |
|
| 2 | |
|
| 3 | |
Corresponding angles are equal.
