Matching: The segments used in reference to the triangle vs. concurrent point. Write the correct letter by
the word.
1. Altitudes
2. Angle bisectors
3. Medians
4. Perpendicular Bisectors
A. Centroid
B. Circumcenter
C. Incenter
D. Orthocenter
1C
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To match the segments used in reference to the triangle with their corresponding concurrent point, we need to understand the definitions and properties of each segment.
1. Altitudes: Altitudes are segments drawn from each vertex of the triangle perpendicular to the opposite side.
2. Angle bisectors: Angle bisectors are segments that divide the angle into two equal parts.
3. Medians: Medians are segments drawn from each vertex of the triangle to the midpoint of the opposite side.
4. Perpendicular Bisectors: Perpendicular bisectors are segments that bisect a side of the triangle at a right angle.
Now let's match these segments with their corresponding concurrent point:
A. Centroid: The centroid is the point of concurrency of the medians. It is the point where all three medians intersect.
B. Circumcenter: The circumcenter is the point of concurrency of the perpendicular bisectors. It is the center of the circle passing through all three vertices of the triangle.
C. Incenter: The incenter is the point of concurrency of the angle bisectors. It is the center of the circle inscribed within the triangle.
D. Orthocenter: The orthocenter is the point of concurrency of the altitudes. It is the point where all three altitudes intersect.
Based on these definitions, the correct matches would be:
1. Altitudes - D (Orthocenter)
2. Angle bisectors - C (Incenter)
3. Medians - A (Centroid)
4. Perpendicular Bisectors - B (Circumcenter)