Question

A rhombus is cut along the diagonals to make four triangles. Which three statements are correct for any rhombus? 1) All four triangles are right-angled. 2) All four triangles are isosceles. 3) All four triangles are congruent. 4) Area of a rhombus = 4 x area of one triangle. 5) Perimeter of rhombus = 4 x perimeter of one triangle.

Answer 1

1). All four triangles are right-angled.

3.) All four triangles are congruent.

4) Area of a rhombus = 4 x area of one triangle.

Explanation:

If a rhombus is cut into four triangles using diagonals, the three statements that would apply to any rhombus would be that 'all those four triangles would be right-angled,' 'the triangles would be congruent to one another,' and 'area of one triangle * 4 would be equal to the area of the rhombus.'

As we know, the diagonals bisect one another in a rhombus at 90° and the angles opposite to one another are equal. This proves that all four triangles constructed through the diagonals would be ≅ through SSS congruency and perpendicular to one another because the corresponding edges of the congruent triangles are also ≅ . Since the rhombus is divided into four equal parts, the area of one triangle into four would be equals to the area of the rhombus. Thus, options 1, 3, and 4 are the correct answers.