Question

16). complete each proof. write the letter and reason of the correct answer from the word bank.
prove ( \triangle acbcong\triangle adb )

word bank (there are extras and can be used more than once)

Explanation:

Step1: Identify the congruent sides

From the figure, we can see that \(CB\) and \(DB\) are marked as equal. So, for statement 2, the correct letter is \(G\) (\(\overline{CB}\cong\overline{DB}\)). The reason is that they are given as equal (from the figure's markings, which is a form of 'Given' information in geometric proofs).

Step2: Consider the common side

For statement 3, the side \(AB\) is common to both \(\triangle ACB\) and \(\triangle ADB\). The letter is \(A\) (\(\overline{AB}\cong\overline{AB}\)) and the reason is the Reflexive Property (a segment is congruent to itself), so the reason is \(B\).

Step3: Apply the right - triangle congruence criterion

Since \(\triangle ACB\) and \(\triangle ADB\) are right - triangles (statement 1), we have a hypotenuse (\(AB\)) and a leg (\(CB\) and \(DB\)) congruent. The congruence criterion for right - triangles is \(HL\) (Hypotenuse - Leg). So, for statement 4, the reason is \(K\).

Answer:

1. \(G\), Given; 3. \(A\), \(B\) (Reflexive Property); 4. \(K\) (HL)