Question

1. for rhombus abcd, which statement about the angles is false?

∠bao ≅ ∠boa
∠doa ≅ ∠doc
∠boa ≅ ∠doc

Explanation:

Step1: Properties of rhombus diagonals

In a rhombus, the diagonals are perpendicular to each other. So, $\angle BOA = \angle DOC=90^{\circ}$ (vertically opposite angles are also equal, so $\angle BOA\cong\angle DOC$). Also, $\angle DOA=\angle DOC = 90^{\circ}$ (diagonals of a rhombus are perpendicular).

Step2: Analyze $\angle BAO$ and $\angle BOA$

$\angle BAO$ is an acute angle (since in right - triangle $ABO$, $\angle ABO+\angle BAO = 90^{\circ}$) and $\angle BOA = 90^{\circ}$. So, $\angle BAO
ot\cong\angle BOA$.

Answer:

$\angle BAO\cong\angle BOA$