- External Tangent Congruence Theorem: Two tangent segments from a common external point are congruent, their segments will be equal or congruent. for example, if SR and ST are tangent segments, then SR = ST
- To prove this theorem, we can use the tangent segment theorem formula which states that the sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse
- An example of this theorem in action is when we have the tangent segments from a point outside a circle being congruent, and we can use the formula to prove their congruence
- Tangent Line to Circle Theorem: If a line is tangent to a circle at a point, then the line is perpendicular to the radius at that point
- To prove this theorem, we can use the formula to find the radius of the circle using the Pythagorean Theorem
- An example of this theorem is when we have a line tangent to a circle at a given point, and we can use the formula to determine the radius of the circle
- Congruent Central Angles Theorem: In the same circle, or in congruent circles, two minor arcs are congruent if and only if their corresponding central angles are congruent
- An example of this theorem is when two circles being congruent, their central angles will determine the congruence of their arcs
- These theorems and formulas are essential tools in solving problems related to tangent segments, tangent lines to circles, and congruent central angles in geometry.
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