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Magazine Chapter 5: Q10 (page 174)
Give the reason for each step in the following proof of theorem 5-6
Given:
Prove: ABCD is a parallelogram.
Proof:
Short Answer
The complete table is:
Statements | Reasons |
; | Given |
The Sum of angles of a quadrilateral is . | |
Divide both sides of the equation by 2. | |
, | If a transversal intersects two lines such that each pair of interior angles on the same side of a transversal are supplementary then the lines are said to be parallel. |
ABCD is a parallelogram | If both pairs of opposite sides of the quadrilateral are parallel, then the quadrilateral is a parallelogram. |
Step by step solution
Step 1. Observe the given diagram.
The given diagram is:
Step 2. Description of step.
It is being given that and .
As, the sum of the angles of the quadrilateral is .
Therefore, it can be obtained that:
Now, divide both sides of the equation by 2.
Therefore, it can be obtained that:
If a transversal intersects two lines such that each pair of interior angles on the same side of a transversal are supplementary then the lines are said to be parallel.
Therefore, it can be said that and .
If both pairs of opposite sides of the quadrilateral are parallel, then the quadrilateral is a parallelogram.
Therefore, ABCD is a parallelogram.
Step 3. Complete the table.
The complete table is:
Statements | Reasons |
Given | |
The Sum of angles of a quadrilateral is . | |
Divide both sides of the equation by 2. | |
If a transversal intersects two lines such that each pair of interior angles on the same side of a transversal are supplementary then the lines are said to be parallel. | |
ABCD is a parallelogram | If both pairs of opposite sides of the quadrilateral are parallel, then the quadrilateral is a parallelogram. |
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