Question 9 of 12intermediate🔍 AnalyzeDiagram4 marks

Construct a rectangle in which one of the diagonals divides the opposite angles into 45° and 45°. What do you observe about the sides?

Correct Answer

When a diagonal divides opposite angles into 45° and 45°, the rectangle becomes a square. All four sides are equal in length. Construction: Step 1: Draw a line segment AB. Step 2: At A, construct a line at 45° to AB. Step 3: At B, construct a perpendicular. Step 4: Mark intersection as C. Step 5: Complete the figure. The resulting figure is a square because when the diagonal divides the angles equally (45° each), it indicates that adjacent sides are equal, which is the defining property of a square.

Exercise: Construct | Q: 2 | (Page Page 25)
For More Understanding

Explanation

The chapter asks students to observe the sides. When a diagonal divides angles into equal parts (45° each), the rectangle must be a square. This is because equal angle division by the diagonal occurs only when adjacent sides are equal, which is the property of a square.

Solution Steps

  1. Step 1: Draw AB.

  2. Step 2: Construct 45° angle at A.

  3. Step 3: Construct perpendicular at B.

  4. Step 4: Find C at intersection.

  5. Step 5: Complete the figure.

  6. Step 6: Observe that all sides are equal - it's a square.

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