Angle AOB+Angle BOC= Angle AOC
To prove that Angle AOB + Angle BOC = Angle AOC, you can analyze the given information using the angles formed by the three points A, O, and C.
Let's break down the proof step-by-step:
1. Start with triangle AOB and draw a line from point O to point C, creating triangle BOC.
2. According to the angle addition postulate, the sum of Angle AOB and Angle BOC will equal Angle AOC, as they share a common side.
3. Therefore, Angle AOB + Angle BOC = Angle AOC.
By following these steps and using the angle addition postulate, you can prove that the sum of Angle AOB and Angle BOC is equal to Angle AOC.
To prove that angle AOB + angle BOC is equal to angle AOC, we can use the fact that the sum of the angles in a triangle is 180 degrees.
First, let's draw a diagram to visualize the situation. Draw triangle ABC with point O inside it. Angle AOB is the angle formed by lines AO and BO, angle BOC is the angle formed by lines BO and CO, and angle AOC is the angle formed by lines AO and CO.
To prove the given statement, we need to show that angle AOB + angle BOC is equal to angle AOC.
Now, let's proceed with the proof. Here's how we can show that angle AOB + angle BOC = angle AOC:
1. Start with triangle ABC and point O inside it.
2. Draw a line from O to A and a line from O to C to form triangle AOC.
3. Since triangle ABC and triangle AOC share side AC, angles BOC and angle AOC are adjacent angles. Therefore, the sum of these adjacent angles is equal to the sum of the angles formed when their measures are added.
4. From step 3, we know that angle AOB + angle BOC must be equal to the sum of the two adjacent angles formed by lines AO and CO (sides of the triangle).
5. Finally, recall that the sum of the angles in a triangle is always 180 degrees. Since angle AOC is an angle in triangle AOC, its measure is 180 degrees minus the sum of the other two angles in the triangle (angle AOB + angle BOC). Therefore, angle AOC = angle AOB + angle BOC.
By following these steps, we have successfully proven that angle AOB + angle BOC = angle AOC.