Question

writing two - column proofs
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^{circ})
□ (m∠cbd = 45^{circ})
□ (m∠abd = 90^{circ})

Explanation:

• A right - angle is marked at ∠ABD, so ∠ABD is a right angle and \(m\angle ABD = 90^{\circ}\).
• Since \(\overrightarrow{BC}\) divides the right - angle ∠ABD into two equal parts (as there is no indication otherwise from the problem's nature of a basic angle - bisector diagram in geometry), \(\overrightarrow{BC}\) bisects ∠ABD.
• If \(\overrightarrow{BC}\) bisects \(\angle ABD\) and \(m\angle ABD=90^{\circ}\), then \(m\angle ABC=\frac{1}{2}m\angle ABD = 45^{\circ}\) and \(m\angle CBD=\frac{1}{2}m\angle ABD = 45^{\circ}\)

Answer:

∠ABD is a right angle, \(\overrightarrow{BC}\) bisects angle ∠ABD, \(m\angle ABC = 45^{\circ}\), \(m\angle CBD = 45^{\circ}\), \(m\angle ABD = 90^{\circ}\)