Question

part a
which angles must have a measure of ( 25 ^ { circ } ) ?
select all that apply.
( angle b a d )
( angle a b d )
( angle b a o )
( angle d a o )
( angle a d b )
part b
for each triangle in the table, use the information given in the figure to identify if the triangle must be isosceles or must be right.
select the if the triangle must be isosceles or right from the drop - down below.
( \triangle a b d )
( \triangle a o d )
( \triangle a b o )

Explanation:

Part A

Step1: Use the property of the inscribed - angle and central - angle

Since \(BD\) is a diameter, \(\angle BAD = 90^{\circ}\) (angle inscribed in a semi - circle). \(OA = OB\) (radii of the same circle), so \(\triangle ABO\) is isosceles. Let \(\angle ABD=\angle BAO = 25^{\circ}\).
We know that \(OA = OD\) (radii of the same circle), but there is no information to suggest that \(\angle DAO = 25^{\circ}\) or \(\angle ADB = 25^{\circ}\) without additional data about the arcs or other angles.

Part B

Step1: Analyze \(\triangle ABD\)

Since \(BD\) is a diameter, by the inscribed - angle theorem (\(\angle BAD = 90^{\circ}\)), \(\triangle ABD\) is a right - triangle.

Step2: Analyze \(\triangle AOD\)

Since \(OA = OD\) (radii of the same circle), \(\triangle AOD\) is isosceles.

Step3: Analyze \(\triangle ABO\)

Since \(OA = OB\) (radii of the same circle), \(\triangle ABO\) is isosceles.

Answer:

Part A

B. \(\angle ABD\), C. \(\angle BAO\)

Part B

\(\triangle ABD\): right - triangle; \(\triangle AOD\): isosceles; \(\triangle ABO\): isosceles