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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the orthocenter of a triangle?
💡 Hint: Think about the altitudes and where they meet.
Question 2
Easy
In which type of triangle is the orthocenter located at a vertex?
💡 Hint: Consider the properties of right angles.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
Where is the orthocenter located in an acute triangle?
- Inside the triangle
- On the vertex of the right angle
- Outside the triangle
💡 Hint: Think about the angles of the triangle.
Question 2
True or False: The orthocenter can be located outside the triangle in every type of triangle.
- True
- False
💡 Hint: Review the definitions of acute, right, and obtuse triangles.
Solve 2 more questions and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
In triangle XYZ, with coordinates X(2, 3), Y(6, 3), and Z(4, 8), find the coordinates of the orthocenter by calculating the altitudes from each vertex.
💡 Hint: Start by determining the slopes and equations of the lines formed by the triangle's vertices.
Question 2
Demonstrate how the orthocenter's location affects the triangle's properties and provide a proof that in any triangle the orthocenter will always relate to the centroid and circumcenter on Euler's line.
💡 Hint: Use coordinate geometry as a basis to establish proofs with calculated distances and angles.
Challenge and get performance evaluation