2. Construct the 3 medians, 3 altitudes, 3 perpendicular bisectors, and 3 angle bisector for each type of triangle


 Blaise Arnold
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1 Using a compass and straight edge (ruler) construct the angle bisectors, perpendicular bisectors, altitudes, and medians for 4 different triangles; a, Isosceles Triangle, Scalene Triangle, and an. The purpose of this project is for you to have a better understanding of the properties of each of these constructions as well as the location of the points of concurrency. Project Directions 1. You must use the triangles provided to you for this project. 2. Construct the 3 medians, 3 altitudes, 3 perpendicular bisectors, and 3 angle bisector for each type of triangle 3. All construction marks should be left on the paper. 4. Use the provided key to identify each construction angle bisectors red perpendicular bisectors blue altitudes  green medians  orange Easiest if you use colored PENCILS to do this. Sharpen your pencils to a good point for best results. 5. All Points of concurrency clearly and labeled. (for each triangle) 6. All congruent segments and should be clearly as well as any right angles. 7. For each triangle, in complete sentences: (to be hand written in the Description section of the template) Name and classify the triangle by angles and sides. Name the points of concurrency of the medians, altitudes, perpendicular bisectors, and angle bisectors for each triangle. Describe the location of the intersection (inside, on, or outside the triangle). 8. Project should be in some type of folder and have a cover page with Name, Date, Period, and attach the given rubric. 9. Project should be neat, accurate, and organized. All lines should be drawn with a ruler, and the vertices of the triangles should be labeled. 10. Once project is completed answer the following questions: (write answers on attached rubric sheet) a) The angles bisector of a triangle is (sometimes, always, or never) the perpendicular bisector. b) The median of the triangle is (sometimes, always, or never) the perpendicular bisector. c) The altitude of the triangle is (sometimes, always, or never) the perpendicular bisector. d) The centriod of a triangle is (sometimes, always, or never) the circumcenter of the triangle. e) The altitude from the vertex angle of an isosceles triangle is (sometime, always, or never) the median. f) The median of any side of an equilateral triangle is (sometimes, always, or never) the angle bisector. g) The altitude of a triangle is (sometime, always, or never) the angle bisector of a triangle h) The incenter of a triangle is (sometime, always, or never) the centroid of a triangle. Additional help with constructions is available in Mr. Leon s room, 3430, at lunch when you make an appointment. LATE PROJECTS WILL BE PENALIZED 20 POINTS FOR EACH DAY LATE. ON TIME MEANS YOU TURN IT IN AT THE BEGINNING OF THE PERIOD IT IS DUE.
2 Constructions Perpendicular Bisector Isosceles Triangle Perpendicular Bisector Scalene Triangle Perpendicular Bisector PerpendicularBisector Intersections Isosceles Triangle Scalene Triangle GEOMETRY TRIANGLE CONSTRUCTION PROJECT RUBRIC Non of the Three constructions Two constructions One construction is constructions are are correct are correct correct correct SCORE Four intersections are correctly drawn Three intersections are correctly drawn Two intersections are correctly drawn One intersection is correctly drawn No intersection is correctly drawn SCORE
3 Descriptions Three of the following are correct: (The triangle is correctly classified, the location of the intersection is given,and the intersection is correctly named) Two of the following are correct: (The triangle is correctly classified, the location of the intersection is given,and the intersection is correctly named) One of the following is correct: (The triangle is correctly classified, the location of the intersection is given,and the intersection is correctly named) None of the following are given: (The triangle is correctly classified, the location of the intersection is given,and the intersection is correctly named) Isosceles Triangle Scalene Triangle SCORE Notation/Organization/Neatness All lines are drawn with a One of the following is missing: (lines are drawn with a Two of the following are missing: (lines are drawn with a Three of the following are missing: (lines are drawn with a Lines are not drawn with a ruler, a key is not included for each not not Acute Triangle Obtuse Triangle SCORE ANSWERS TO QUESTION IN #10. a) Questions SCORE: b) c) d) e) PROJECT : /100 f) g) h) Project is on time. (20)
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Classifying Triangles Student Probe How are triangles A, B, and C alike? How are triangles A, B, and C different? A B C Answer: They are alike because they each have 3 sides and 3 angles. They are different
More informationCOORDINATE GEOMETRY. 13. If a line makes intercepts a and b on the coordinate axes, then its equation is x y = 1. a b
NOTES COORDINATE GEOMETRY 1. If A(x 1, y 1 ) and B(x, y ) are two points then AB = (x x ) (y y ) 1 1 mx nx1 my ny1. If P divides AB in the ratio m : n then P =, m n m n. x1 x y1 y 3. Mix point of AB is,.
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