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Geometry Problems

Please provide detailed answers.

* Can a right triangle be scalene, isosceles, or equilateral? Why or why not? What are the advantages and disadvantages of classifying triangles by sides or angles?

* Describe the relationship between a triangle's centroid and orthocenter. Do they need to be inside the triangle?

* How would you explain the difference between angle-angle-side, angle-side-angle, and side-angle-side to a classmate who thinks the letters look alike?

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* Can a right triangle be scalene, isosceles, or equilateral? Why or why not? What are the advantages and disadvantages of classifying triangles by sides or angles?

Answer: A right angle can be scalene. It is because a right angle can have different side lengths and have different interior angles. The 3-4-5 right triangle is one example. A right triangle can be isosceles. It is because there is a right triangle that has 2 equal sides as well as two interior angles, which is the 45-degree right triangle. A right triangle cannot be an equilateral triangle. It is ...

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