Final answer:
In a triangle, drawing an altitude from vertex A to side BC creates right angles at ∠BAD and ∠ADB. Without additional information, we cannot determine the exact length of BD, though option B is the closest with given choices.
Step-by-step explanation:
In a triangle, when you draw an altitude from vertex A to side BC and label the point it meets side BC as point D, there are a few possibilities to consider. The altitude is a perpendicular line from a vertex to the opposite side, therefore ∠BAD would be 90° since it is where the altitude from A touches side BC. Now, since the altitude is perpendicular, ∠ADB would also be a right angle, 90°.
The length of BD cannot be determined from this information alone without additional measurements or information about the triangle. If it were an isosceles triangle with vertex A being one of the two equal angles, then BD could potentially be half the length of BC, but that is not given in the question. Therefore, given the choices provided, the only factual information we can ascertain is that ∠BAD and ∠ADB are both 90°, and option A is incorrect because BD = BC is an assumption without basis. Option B suggests BD is half of BC and ∠ADB is 45° which is possible but not definitive. Options C and D also state specific measures for angles and lengths without adequate information to confirm them.
By the process of elimination and understanding the properties of an altitude, we can determine that the best answer, without additional information, is the one that confirms the right angles created by the altitude: Option B (∠BAD = 90°, ∠ADB = 90°, BD = 0.5 * BC).