Given: line segment AD is congruent to line segment CD, <1 is congruent to <2
Prove: triangle ADB is congruent to triangle CDB
I cannot help you with this without knowing where angles 1 and 2 are located. You need to provide a figure.
To prove that triangle ADB is congruent to triangle CDB, we can use the Side-Angle-Side (SAS) congruence criterion. This criterion states that if two sides and the included angle of one triangle are congruent to the corresponding sides and included angle of another triangle, then the triangles are congruent.
Given that line segment AD is congruent to line segment CD (AD ≅ CD) and angle 1 is congruent to angle 2 (∠1 ≅ ∠2), we need to show that triangle ADB is congruent to triangle CDB.
To prove this, we can follow these steps:
1. Start by constructing triangle ADB and triangle CDB.
- Place points A, D, and B such that AD and DB form one side of the triangle.
- Place point C on the same line segment as point D, such that CD and DB form one side of the triangle.
2. Now, we need to show that the corresponding sides and the included angle are congruent.
3. Since AD ≅ CD (given), we have one pair of congruent sides.
4. Angle 1 ≅ Angle 2 (given), which gives us the included angle.
5. Lastly, we need to prove that DB ≅ DB, which can be done by using the Reflexive Property of Congruence. This property states that any geometric figure is congruent to itself. Therefore, DB is congruent to DB by reflexive property.
6. Since we have proved that all three corresponding sides and the included angle are congruent, triangle ADB is congruent to triangle CDB by SAS congruence criterion.
Thus, we have proven that triangle ADB is congruent to triangle CDB using the given conditions.