Question

practice. write a 2 - column proof for the following problems. extra credit - 10 pts 11. given: \\( \angle a d b \\) and \\( \angle c d b \\) are right angles \\( \angle a \cong \angle c \\) prove: \\( \triangle a d b=\triangle c d b \\)

Explanation:

Step1: State the given information

Given: $\angle ADB$ and $\angle CDB$ are right angles (so $\angle ADB=\angle CDB = 90^{\circ}$), $\angle A\cong\angle C$

Step2: Identify the common side

In $\triangle ADB$ and $\triangle CDB$, side $BD = BD$ (reflexive property: a segment is congruent to itself)

Step3: Apply AAS (Angle - Angle - Side) congruence criterion

Since we have two angles ($\angle A\cong\angle C$, $\angle ADB\cong\angle CDB$) and a non - included side ($BD$) congruent, by AAS congruence criterion, $\triangle ADB\cong\triangle CDB$

Answer:

Statements	Reasons
2. $\angle ADB=\angle CDB = 90^{\circ}$	Definition of right angles
3. $\angle A\cong\angle C$	Given
4. $BD = BD$	Reflexive property of congruence
5. $\triangle ADB\cong\triangle CDB$	AAS (Angle - Angle - Side) congruence criterion