Answer:
See explanation
Step-by-step explanation:
Statements Reasons
1. Given
2. As alternate interior angles when parallel lines AD and BC intersect by ltransversal BD
3. Given
4. Reflexive property
5. SAS postulate
6. Corresponding parts of congruent triangles are congruent
7. Inverse alternate interior angles theorem
Answer:
Step-by-step explanation:
Since Segment BOA is a diameter:
Arc Ac and Arc CB are in a ratio of two to four. Since Segment BOA is a diameter, Arc ACB measures 180°. Letting the unknown value be <em>x</em>, we can write that:
Hence:
Thus, Arc CB = 120°. By the Inscribed Angle Theorem:
Therefore, ΔABC is a 30-60-90 triangle. Its sides are in the ratios shown in the image below.
Since AC is opposite from the 30° triangle, let AC = <em>a</em>.
We are given that AC = 9. Hence, <em>a</em> = 9.
BC is opposite from the 60° angle and it is given by <em>a</em>√3. Therefore:
