Question

Given: AB > BD, ∠ADB = 2∠C
Prove: AD > DC

Answer 1

To prove that AD > DC, we can use the Law of Sines in triangle ADC and the given information of AB > BD and ∠ADB = 2∠C.

Step-by-step explanation:

To prove that AD > DC, we will use the given information that AB > BD and ∠ADB = 2∠C. We will assume that AB = x and BD = y. Since ∠ADB = 2∠C, we can deduce that ∠ADC = ∠C. Now, using the Law of Sines in triangle ADC, we can write the following equation:

1. Sin ∠ADC / AD = Sin ∠C / CD
2. Sin ∠C / AD = Sin ∠C / CD
3. AD = CD

So, AD is equal to CD. However, since AB > BD, it implies that AD > CD as well. Therefore, the statement AD > DC is proven.