Question

Given abcd is a rhombus, which of the following pairs of triangles are congruent?

1) ABD and BCD
2) ABC and ABD
3) ABC and BCD
4) ACD and BCD

Answer 1

The congruent triangle pairs in a rhombus are ABC and BCD, mirrored across a diagonal.

Step-by-step explanation:

To answer the question of which pairs of triangles are congruent in a rhombus, we must remember that a rhombus has all sides of equal length. When we draw diagonals in a rhombus, we divide it into four triangles, two pairs of which are congruent due to the symmetry of a rhombus.

Looking at the options provided: Option 1 (ABD and BCD) cannot be right because while they share a base, their third sides are different sides of the rhombus. Option 2 (ABC and ABD), these cannot be congruent since triangle ABC includes side AC, while triangle ABD includes side AD, different sides of the rhombus. Option 3 (ABC and BCD), these triangles are congruent because they are mirror images of each other across the diagonal BD of the rhombus. Option 4 (ACD and BCD) can be disregarded for the same reason as the first option, their third sides are different sides of the rhombus.