Question

Given: \angle ADB∠ADB is a right angle.

Prove: \angle ADB \cong \angle CDB∠ADB≅∠CDB.

Answer 1

To prove ∠ ADB ≅ ∠ CDB, one must demonstrate they have the same measure. Since both are right angles, they are congruent as all right angles equal 90 degrees.

Step-by-step explanation:

The question involves proving that ∠ ADB ≅ ∠ CDB, where ∠ ADB is known to be a right angle. From the information provided, it is suggested that ∠ ADB and ∠ CDB share the same vertex D and are both right angles, as the description hints at them being related to right-angled triangles. If both angles are right angles, they are congruent because all right angles are equal to 90 degrees.

Remember, two angles are congruent if they have the exact same measure. Therefore, without loss of generality, if one angle is given as a right angle, the other angle is also a right angle and hence, the two angles are congruent. This is a fundamental property in geometry supported by the postulate that all right angles are equal.

The final answer, in conclusion, is simply to state that since both ∠ ADB and ∠ CDB are right angles, they are congruent by the definition of congruency for angles.

Answer 2

To prove that angle ADB is congruent to angle CDB, we show that both angles are right angles and therefore must be congruent since they both measure 90 degrees. This proof relies on the concept that the sum of angles in a straight line is 180 degrees, and that right angles are defined as 90 degrees.

Step-by-step explanation:

To prove that angle ADB is congruent to angle CDB, we begin by examining the given information that angle ADB is a right angle. By definition, a right angle is 90 degrees. If angle ADB is a right angle, then any other angle that is supplementary to angle ADB in a linear pair must also be 90 degrees to maintain the 180 degrees in a straight line.

Therefore, it follows that if angle ADB is a right angle, then angle CDB, being adjacent and supplementary to angle ADB, must also measure 90 degrees, making it a right angle as well. Since both angles ADB and CDB are right angles, they are equal in measure, which means they are congruent.

To formally complete the proof, one could use the fact that the sum of angles in a straight line is 180 degrees, and supplementary angles are angles that add up to 180 degrees:

1. angle ADB is a right angle (given).
2. angle ADB + angle CDB = 180 degrees (straight line).
3. angle ADB = angle CDB = 90 degrees (definition of a right angle).
4. Therefore, angle ADB is congruent to angle CDB (angles with equal measures are congruent).