Question

which information do you know is true from the diagram? check all that apply.
∠abd is a right angle.
(overrightarrow{bc}) bisects angle ∠abd.
m∠abc = 45°
m∠cbd = 45°
m∠abd = 90°

Explanation:

• For $\angle ABD$: The diagram shows a right - angle symbol at $\angle ABD$, so $\angle ABD$ is a right angle, meaning $m\angle ABD = 90^{\circ}$.
• For $\overrightarrow{BC}$: Since $\angle ABD = 90^{\circ}$ and the diagram implies that $\overrightarrow{BC}$ splits $\angle ABD$ into two equal angles (as the two smaller angles look equal), $\overrightarrow{BC}$ bisects $\angle ABD$.
• For $m\angle ABC$ and $m\angle CBD$: Since $\overrightarrow{BC}$ bisects the $90^{\circ}$ angle $\angle ABD$, each of the angles $\angle ABC$ and $\angle CBD$ is $\frac{90^{\circ}}{2}=45^{\circ}$.
• The right - angle symbol confirms $\angle ABD$ is a right angle.

Answer:

• $\boldsymbol{\angle ABD}$ is a right angle.
• $\boldsymbol{\overrightarrow{BC}}$ bisects angle $\boldsymbol{\angle ABD}$.
• $\boldsymbol{m\angle ABC = 45^{\circ}}$
• $\boldsymbol{m\angle CBD = 45^{\circ}}$
• $\boldsymbol{m\angle ABD = 90^{\circ}}$