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Practice Problems ( Wks19) NAME ______________________ DATE _______________ B Medians D F G C E A B Midsegments F D C E A C b2 h3 b1 h1 B Altitudes h2 b3 A Angle Bisectors Perpendicular Bisectors Honors Geometry Medians #1 Livingston High School Mathematics Department Mr. Lamb, Mr. Memory NAME _____________________ Medians, Altitudes, Angle Bisectors, Bisectors The point of intersection of the medians of a triangle is called the centroid. The point of intersection of the altitudes of a triangle is called the orthocenter. The point of intersection of the angle bisectors of a triangle is called the incenter. The point of intersection of the perpendicular bisectors of a triangle is called the circumcenter.. Fill in the following with the correct word: (Use the words above for some of the choices.) 1. The __________________ separates the three segments into sub-segments that have a 2 to 1 ratio. 2. The __________________ is equidistant to the sides of the triangle. 3. When drawing a circle around the vertices of a triangle, locate its _______________ . 4. Which of the points is the center of balance of the triangle? ______________ Why does it balance at this point? ______________________________________ 5. The _________________, _________________, and ____________________ are always collinear on a line called the Euler line. 6. If a triangle has three congruent medians then the triangle is ___________________. 7. If none of the altitudes are congruent, the triangle must be __________________. 8. The _____________________ of a triangle separates the triangle into two triangles with equal areas. 9. In a triangle, the product of any side and its ____________________ to that side is equal to the product of any other side and the ___________________ to that side. The product is always equal to ________________ the area. 10. In a _____________________ triangle, the altitudes do not meet in a point. 11. In a right triangle, the perpendicular bisectors meet at the ____________________ _________________________ while the altitudes meet at the ________________. 12. Any point on the ___________________ of a triangle is equidistant from the adjacent sides of the bisected __________________. 13. The ____________________________ of a triangle separates the side to which it is drawn into two segments whose ratio is equal to the ratio of the remaining two sides. Honors Geometry Medians #1 Livingston High School Mathematics Department Mr. Lamb, Mr. Memory 14. The ___________________________ of a triangle separate the side to which it is drawn into two segments whose ratio is equal to the ratio of the areas of the two triangles that are formed. 15. The perpendicular bisectors of a triangle will have one bisector pass through a vertex of the triangle only if __________________________________________________. 16. The intersection of the _______________________________ of a triangle is the center of inscribed circle. 17. The intersection of the _______________________________ of a triangle is the center of circumscribed circle. 18. The _____________________ drawn from the vertex of the right angle of a right triangle creates two isosceles triangles with equal areas. Explain why. __________ ___________________________________________________________________. 19. In an obtuse triangle the ______________________ and _______________________ meet outside the triangle, while the ____________________ and ________________ meet inside the triangle. 20. Any point on the ________________________ is equidistant from the endpoints of the segment. Any point on the ________________________ is equidistant from the sides of the angle. 21. Use your knowledge of the Pythagorean Theorem and the special segments within a triangle to solve the following problem. B In the diagram at right, AE and BD are altitudes. AB = 20, BC = 20 and DE = 12. a. What is the length of BE? ______ D b. What is the area of ABC? _______ c. What is the perimeter of ABC? _______ A C E d. What is the length of AD? ________ e. Radius of inscribed circle for ABC = ______ Honors Geometry Medians #1 Livingston High School Mathematics Department Mr. Lamb, Mr. Memory