Question 7 of 13intermediate🔧 ApplyNumerical3 marks

Find all the sides and the angles of the quadrilateral obtained by joining two equilateral triangles with sides 4 cm.

Correct Answer

Given: Two equilateral triangles with side 4 cm are joined along a common side.

Step 1: Identify that joining two equilateral triangles creates a quadrilateral with four equal sides.

Step 2: Each side equals 4 cm (the side of the equilateral triangles).

Step 3: The angles at the joining vertices are 60° + 60° = 120° each.

Step 4: The other two angles remain 60° each.

Step 5: Verify: opposite angles are equal (60° and 120°), and adjacent angles sum to 180°.

Answer: The quadrilateral is a rhombus with:

  • All sides = 4 cm
  • Angles = 60°, 120°, 60°, 120°
Exercise: Figure it Out (Section 3) | Q: 1 | (Page Page 26)
For More Understanding

Explanation

When two equilateral triangles of side 4 cm are joined along a common side, the resulting quadrilateral has all four sides equal to 4 cm (a rhombus). The angles at the two vertices where the triangles meet are each 60° + 60° = 120°. The other two angles remain 60° each. In a rhombus, opposite angles are equal and adjacent angles sum to 180°, which is satisfied: 60° + 120° = 180°.

Solution Steps

  1. Step 1: Identify that joining two equilateral triangles creates a quadrilateral with four equal sides.

  2. Step 2: Each side equals 4 cm (the side of the equilateral triangles).

  3. Step 3: The angles at the joining vertices are 60° + 60° = 120° each.

  4. Step 4: The other two angles remain 60° each.

  5. Step 5: Verify: opposite angles are equal (60° and 120°), and adjacent angles sum to 180°.

PreviousNext