Question

youre creating a banner to hang in the back of the taco truck as a backdrop. you place two equilateral triangles together, aligning one side of each triangle. what shape do the two triangles form? square rectangle hexagon rhombus

Explanation:

An equilateral triangle has all sides equal and each angle equal to \(60^{\circ}\). When two equilateral triangles are joined along one side:

• A square has four right angles (\(90^{\circ}\)). Since the angles of the combined shape from the equilateral triangles are \(60^{\circ}+60^{\circ} = 120^{\circ}\) (at non - joined vertices) and \(60^{\circ}\) is not \(90^{\circ}\), it's not a square.
• A rectangle has four right angles. Using the same angle - reasoning as for the square, it's not a rectangle.
• A hexagon has six sides. When we join two equilateral triangles along one side, we have \(3 + 3-2=4\) sides (we lose 2 sides as they are joined), so it's not a hexagon.
• A rhombus has four sides of equal length. When two equilateral triangles (with all sides equal) are joined along one side, the resulting shape has four sides of equal length. Also, the opposite angles of the resulting shape are equal (\(60^{\circ}\) and \(120^{\circ}\) pairs), which is a property of a rhombus.

Answer:

Rhombus