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Honors Geometry

Honors Geometry. Unit 4 Project 1 - Part 5. Part 5A. On a sheet of paper, construct a scalene triangle of sides 14cm, 12cm and 10cm. Label the vertices A, B, and C. Find the midpoint of AC, BC and AB. Label these midpoints P, Q and R, respectively.

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Honors Geometry

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  1. Honors Geometry • Unit 4 Project 1 - Part 5

  2. Part 5A • On a sheet of paper, construct a scalene triangle of sides 14cm, 12cm and 10cm. • Label the vertices A, B, and C. • Find the midpoint of AC, BC and AB. • Label these midpoints P, Q and R, respectively. • Draw perpendicular lines through P, Q and R. • These lines will not necessarily pass through any of the vertices of the triangle

  3. Part 5A Analysis • Answer the question on the answer sheet.

  4. Part 5B • Label the Point of Concurrency S • Draw segments AS, BS and CS • Measure AS, BS and CS and record

  5. Part 5C • Using your compass, draw a circle with a center at S that contains points A, B and C • Record your observations

  6. Part 5D • Repeat Parts 5A, 5B and 5C for: • An obtuse scalene triangle • A right scalene triangle • An isosceles triangle • An equilateral triangle • Record your observations on the answer sheet.

  7. Part 5E • Each member of the group is to draw 3 segments such that all nine are different lengths, label them each AB. • Find the midpoints of each segment and label teach of them M. • Then draw a perpendicular line through each of the midpoints • Pick a points on each perpendicular line and label it C • draw segments AC and BC • Measure AC and BC and record on the answer sheet

  8. Part 5E (cont.) • Pick another point on the perpendicular line and label it D • draw segments AD and BD • Measure AD and BD and record on the answer sheet • Answer the follow up question on the answer sheet

  9. Perpendicular Bisector(of a segment!) • A line, ray or segment that is perpendicular to and bisects a segment is a perpendicular bisector of the segment.

  10. The Perpendicular Bisector Theorem • Any point on the perpendicular bisector of a segment is equidistant form the end points of the segment.

  11. The Perpendicular Bisectors and a triangle • The point of concurrency of the of the perpendicular bisectors is called the circumcenter • The circumcenter is the center of the circumscribed circle aka the circumcircle. (circumscribed - to be drawn around)

  12. Part 6A • Looking through all of the triangles you have produced so far, choose the type whose points of concurrency are: • separate points • all on the interior of the triangle • Check with the instructor before continuing on to the nect step

  13. Step 6B • Each student is to do the following! • On each of 4 notecards (one triangle per card), draw congruent triangles of the type chosen on the previous page (draw them reasonably large - try to fill most of the card) • one the first card, draw the 3 medians • one the second card, draw the 3 altitudes • one the third card, draw the 3 angle bisectors • one the fourth card, draw the 3 perp. bisectors

  14. Part 6B (cont.) • Cut out each of the triangles drawn on your cards • poke a pin hole through the point of concurrency in each triangle • cut 4 lengths of orange string about 4-6in. long • thread the string through the hole and tie a knot

  15. Part 6B (cont.) • Hang each triangle by its string and observe what happens • Record your observations on the answer sheet

  16. Part 6B Analysis • Answer the questions on the answer sheet

  17. Project Analysis • Type up the following: • What did you learn from this project? • (separate paragraph per team member!)

  18. To turn-in • Due Tuesday, January 11, 2011 • All answer sheets • All triangles produced including the Cut-out triangles • Personal Reflections

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