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Which of the following statement is CORR...

Which of the following statement is CORRECT ?

A

A unique quadrilateral can be constructed if its two sides and a diagonal is given .

B

A unique quadrilateral can be constructed if its two adjacent sides and two angles are given .

C

A unique quadrilateral can be constructed if its three sides and two included angles are given .

D

None of these

Text Solution

AI Generated Solution

The correct Answer is:
To determine which statement about constructing a unique quadrilateral is correct, we will analyze each option step by step. ### Step 1: Analyze Option 1 **Statement:** A unique quadrilateral can be constructed if two sides and a diagonal are given. - **Explanation:** A quadrilateral has four sides, and to uniquely determine it, we need at least five measurements (sides, angles, diagonals). Here, we only have two sides and one diagonal, which totals three measurements. Therefore, this statement is **incorrect**. ### Step 2: Analyze Option 2 **Statement:** A unique quadrilateral can be constructed if two adjacent sides and two angles are given. - **Explanation:** In this case, we have two sides and two angles, which gives us a total of four measurements. However, this is not sufficient to uniquely determine a quadrilateral, as we still need at least five measurements. Therefore, this statement is also **incorrect**. ### Step 3: Analyze Option 3 **Statement:** A unique quadrilateral can be constructed if three sides and two angles are given. - **Explanation:** Here, we have three sides and two angles. The three sides provide sufficient information, and the two angles can help in determining the shape of the quadrilateral. This meets the requirement of having at least five measurements (three sides + two angles = five). Therefore, this statement is **correct**. ### Step 4: Analyze Option 4 **Statement:** None of these. - **Explanation:** Since we have found that option three is correct, this statement is **incorrect**. ### Conclusion The correct answer is **Option 3**: A unique quadrilateral can be constructed if three sides and two angles are given. ---
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