Subjects geometry

Joined Equilateral Quad

Step-by-step solutions with LaTeX - clean, fast, and student-friendly.

Search Solutions

Joined Equilateral Quad


1. **Problem Statement:** We have two equilateral triangles each with side length 8 cm. We want to join these two triangles to form a quadrilateral and identify the type of quadrilateral formed. 2. **Joining Two Equilateral Triangles:** If we join two equilateral triangles along one of their sides (each side 8 cm), we create a four-sided figure because the two triangles share one side. 3. **Shape of the Quadrilateral:** The two triangles are both equilateral (all sides 8 cm, all angles 60°). Joining them along one side creates a shape with 4 sides: two sides are the unshared sides of one triangle and the other two sides come from the unshared sides of the second triangle. 4. **Angles in the Quadrilateral:** Since the triangles meet along one side, the angle between the two triangles at the joined side is $60^{\circ} + 60^{\circ} = 120^{\circ}$ (because the internal angles adjacent to the joined side are both 60°). The other angles remain 60°, 60°, and the joined side angles 120°. 5. **Identifying Quadrilateral Type:** - The quadrilateral has two pairs of equal sides: four sides of length 8 cm. - Two angles measure 60°, two angles measure 120°. This matches the definition of a **rhombus**: all sides equal in length, opposite angles equal, and adjacent angles supplementary (60° + 120° = 180°). 6. **Conclusion:** Joining two equilateral triangles of side length 8 cm along one side forms a rhombus with sides 8 cm and interior angles 60° and 120°. **Final answer:** The quadrilateral formed is a rhombus.