Postulate 10-2: Arc Addition Postulate simple definition
The Arc Addition Postulate states that the measure of the sum of two arcs is equal to the measure of their combined arc.
The Arc Addition Postulate states that if two arcs on a circle are not overlapping or adjacent, then the measure of the combined arcs is equal to the measure of the larger arc minus the measure of the smaller arc.
The Arc Addition Postulate states that the measure of the sum of two arcs on a circle is equal to the measure of the arc that is formed when the two arcs are combined.
To understand this postulate, we need to understand a few basic concepts:
1. Arc: An arc is a curved line on a circle that connects two points. It is a part of the circumference of the circle.
2. Measure of an Arc: The measure of an arc is the angle formed by two radii (plural for radius) that connect the center of the circle to the two endpoints of the arc. It is usually measured in degrees.
Now, let's look at the Arc Addition Postulate in a simple way:
Suppose we have a circle with two arcs, let's say Arc AB and Arc BC. The Arc Addition Postulate states that the measure of Arc AB added to the measure of Arc BC is equal to the measure of the arc that is formed when we combine Arc AB and Arc BC.
Mathematically, we can write this as:
The measure of Arc AB + The measure of Arc BC = The measure of Arc AC
Essentially, this postulate tells us that when we combine two arcs on a circle, the resulting arc has a measure equal to the sum of the individual measures of the two arcs.
To apply this postulate, we must know the measures of individual arcs and then add them together to find the measure of the combined arc.