I just took the test! 100% promised. If you don’t believe me then I feel you. It’s hard to trust people on the internet, but if you use it, thank you! Walkthrough: 1. B, Concurrency of perpendicular 2. B, F is the incenter. D, F is the concurrency point of the angle. F, F is equidistant from the three sides of. 3. B, straight 4. B, (1.5, 1) 5. D, (3.5, 3) 6. A, isosceles Part B: D, 122 7. C, 80 8. Part A: A, x=2 Part B: D, 7 units
According to the problem, we were asked to find the name of the theorem that explains why the circumscribed center is equidistant from the vertices of a triangle A. Vertical angle theorem: The vertical angle theorem concerns the angles formed when two straight lines intersect a at the other. So it’s not the right option. B. Concurrency theorem of perpendicular bisectors Bisectors passing through the same point called the circumscribed center of the triangle. The point of intersection is always equidistant from the endpoints. Hence the theorem “B. Concurrency theorem of perpendicular bisectors” explains why the circumscribed center is equidistant from the vertices of a triangle. C. Concurrency of the angle bisector theorem: This gives the center of the triangle. D. Theorem of alternating interior angles This theorem states that if two parallel lines are intersected by a line, then the alternating interior angles are congruent.
Answer 6
The circumscribed center is the center of the circle that passes through the three vertices of the triangle. Remember that all the radii of a circle are congruent, that is, equal to each other. This is why the circumscribed center is equidistant from the vertices of the triangle.
The proof is explained step by step. Walkthrough: The center of the circle is the point at which the perpendicular bisector of the sides of the triangle intersects inside the circle. These points are inside the triangle, just like on the circle, and the vertices of the triangles are on the circle. Therefore, the distance between the circumscribed center and the vertices is called the radius of the circle, which is always equidistant from the center. Therefore, the circumscribed center is equidistant from the vertices of a triangle.
The answer is B. Recall the definition of the circumscribed center of a triangle: the intersection of the perpendicular bisectors. If we draw a line perpendicular to each of the three sides, these three lines intersect at a common point and the distance from this point to the three vertices is equal, which can be proved using similar triangles. If we draw a circle with the circumscribed center of the triangle as the center and the distance from the circumscribed center to the vertices as the radius, the triangle will be inscribed in the circle.
Answer 6
The circumscribed center is the center of the circle that passes through the three vertices of the triangle. Remember that all the radii of a circle are congruent, that is, equal to each other. This is why the circumscribed center is equidistant from the vertices of the triangle.
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