Question 6 of 12advanced🔧 ApplyDiagram4 marks

Construct a rectangle in which one of the diagonals divides the opposite angles into 60° and 30°.

Correct Answer

To construct a rectangle where a diagonal divides opposite angles into 60° and 30°: Step 1: Draw a line segment AB of arbitrary length. Step 2: At point A, construct a line making 60° with AB (or 30°, depending on which angle is needed first). Step 3: Draw a perpendicular to AB at point B. Step 4: The intersection of the 60° line from A and the perpendicular from B gives point C. Step 5: Complete the rectangle by drawing perpendicular at A and marking D such that AD = BC. Step 6: Join diagonal AC. Verify that diagonal AC divides angle A into 60° and 30°, and divides angle C similarly.

Exercise: Construct | Q: 1 | (Page Page 19)
For More Understanding

Explanation

The chapter provides a detailed solution with steps. The key insight is that if a diagonal divides one angle into 60° and 30°, it must divide the opposite angle similarly. The construction uses perpendicular lines and angle construction techniques.

Solution Steps

  1. Step 1: Draw AB with arbitrary length.

  2. Step 2: At A, draw a line at 60° to AB.

  3. Step 3: At B, draw a perpendicular to AB.

  4. Step 4: Mark intersection point C.

  5. Step 5: Complete rectangle by drawing perpendicular at A.

  6. Step 6: Mark D and join CD.

  7. Step 7: Draw diagonal and verify angle divisions.

PreviousNext