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Special Triangle Points Quiz
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Special Triangle Points Quiz
📚 Part 1: Multiple Choice & Vocabulary
Instructions: Choose the best answer for each question. Fill in the circle completely.
1. The point where all three medians of a triangle intersect is called the:
A) Circumcenter
B) Incenter
C) Centroid
D) Orthocenter
2. Which special point is equidistant from all three vertices of a triangle?
A) Centroid
B) Circumcenter
C) Incenter
D) Orthocenter
3. The incenter is formed by the intersection of:
A) Angle bisectors
B) Perpendicular bisectors
C) Medians
D) Altitudes
4. In an obtuse triangle, which special point lies outside the triangle?
A) Centroid
B) Incenter
C) Circumcenter
D) All of the above
5. A median of a triangle connects:
A) A vertex to the opposite side's midpoint
B) Two midpoints of sides
C) A vertex to the opposite side perpendicularly
D) The centers of two sides
✏️ Part 2: Fill in the Blanks & Short Answer
6. The _____________ divides each median in a 2:1 ratio.
7. The center of the inscribed circle of a triangle is called the _____________.
8. The point where all three altitudes meet is the _____________.
9. In a right triangle, the circumcenter is located at the _____________ of the hypotenuse.
10. Explain why the incenter is always inside any triangle:
🔍 Part 3: Problem Solving
11. If the centroid of a triangle is at point G(4, 6), and two vertices are A(2, 3) and B(8, 9), find the coordinates of vertex C. Show your work:
12. In triangle DEF, if the circumcenter is equidistant from all vertices and the distance from the circumcenter to vertex D is 10 units, what is the radius of the circumscribed circle?
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