[url=https://docs.google.com/document/d/1vw2vI4oCPxDNuN3e8HpF85rnl6WtfMyPtBMZnc49cQ4/copy][color=#9900ff][size=150][center]Handout for this activity.[/center][/size][/color][/url]

[size=200][color=#9900ff]Part 2: Large Triangles [/color][size=100][i](You may work on this with a classmate) [/i][/size][/size][list=1][*]Ask your teacher for a large whiteboard triangle[/*][*]Draw the three MEDIANS for the triangle [br](connect each vertex to the midpoint of the opposite side)[/*][*]Label the CENTROID of the triangle[/*][*]Try to balance the triangle at the centroid[/*][/list]

[table][tr][td][list=1][*]Measure ([b]in centimeters)[/b] and label the length of each segment of each median (6 segments total)[br][br][/*][*]Upload a picture of your triangle to Google Classroom [br][b](Task 3)[/b][br][br][/*][*]Write a conjecture about the lengths of the segments you measured.[br][br][i]Hint: compare BX to XF, AX to XE and DX to CX[/i][/*][/list][br][/td][td][img]https://www.geogebra.org/resource/jxcsnspt/L4hZLe6CqFlg2A2i/material-jxcsnspt.png[/img][br][br][/td][/tr][/table]

[color=#ff0000][b][i][size=150][size=200]>>> Record your conjecture on your handout paper.[/size][/size][/i][/b][/color]

[size=200][color=#9900ff]Part 3: Euler Line[/color][/size]

[b][size=150]Task 4[/size][/b][list=1][*]Show only the [u]Perpendicular Bisectors[/u] of sides ([b]circumcenter[/b])[/*][*]Drag a vertex to experiment with different types of triangles [br][i](scalene, isosceles, acute, right, obtuse, equiangular/equilateral)[/i][/*][/list][br][color=#cc0000]Write a conjecture for the location of the CIRCUMCENTER of a triangle.[br] [/color][size=50][size=150][u][size=85]Your conjecture could be like this:[br][/size][/u][/size][/size][center][size=150][color=#0000ff]The location of the circumcenter [/color][color=#0000ff]is _____ an acute triangle,[br] _____ a right triangle, and _____ an obtuse triangle. [/color][/size][size=85][b][br][choices: inside, outside, on][/b][/size][/center][color=#ff0000][b][i][size=150][size=200]>>> Record your conjecture on your handout paper.[/size][/size][/i][/b][/color]

[b][size=150]Task 5[/size][/b][br][list=1][*]Show only the Lines Containing Altitudes ([b]orthocenter[/b])[/*][*]Drag a vertex to experiment with different types of triangles [br][i](scalene, isosceles, acute, right, obtuse, equiangular/equilateral)[/i][/*][/list][br][color=#cc0000]Write a conjecture for the location of the ORTHOCENTER of a triangle (inside, outside, or on the triangle).[/color][color=#ff0000][b][i][size=150][size=200][br][br]>>> Record your conjecture on your handout paper.[/size][/size][/i][/b][/color]

[b][size=150]Task 6[/size][/b][list=1][*]Show only the Angle Bisectors ([b]incenter[/b])[/*][*]Drag a vertex to experiment with different types of triangles [br][i](scalene, isosceles, acute, right, obtuse, equiangular/equilateral)[/i][/*][/list][br][color=#cc0000]Write a conjecture for the location of the INCENTER of a triangle (inside, outside, or on the triangle).[/color][color=#ff0000][b][i][size=150][size=200][br]>>> Record your conjecture on your handout paper.[/size][/size][/i][/b][/color]

[b][size=150]Task 7[br][/size][/b][list=1][*]Show only the Medians ([b]centroid[/b])[/*][*]Drag a vertex to experiment with different types of triangles [br][i](scalene, isosceles, acute, right, obtuse, equiangular/equilateral)[/i][/*][/list][br][color=#cc0000]Write a conjecture for the location of the CENTROID of a triangle (inside, outside, or on the triangle).[br][/color][color=#ff0000][b][i][size=150][size=200][br]>>> Record your conjecture on your handout paper.[/size][/size][/i][/b][/color]

[b][size=150]Task 8[br][/size][/b][list=1][*]Leave the [b]centroid[/b] marked and show the [b]centroid measurements[/b].[/*][*]Test your hypothesis from [b]Part 2: Large Triangles.[/b][/*][/list][br][color=#cc0000]Did the measurements verify your hypothesis?[br][b] [i]If not, write a new hypothesis comparing the distances.[br][/i][/b][/color][color=#ff0000][b][i][size=150][size=200][br]>>> Record your conjecture on your handout paper.[/size][/size][/i][/b][/color]

[b][size=150]Task 9[br][/size][/b]The [b]Euler Line[/b] is named after an 18th century mathematician [url=https://en.wikipedia.org/wiki/Leonhard_Euler]Leonhard Euler[/url][i] (pronounced 'oiler')[br][br][/i][color=#cc0000]Which of the four special points [/color][size=85][orthocenter, circumcenter, incenter, centroid][/size][color=#cc0000] are [u]always[/u] on the Euler Line. [/color][i](these points are [u]collinear[/u])[br][/i][br][color=#ff0000][b][i][size=150][size=200]>>> Record your conjecture on your handout paper.[/size][/size][/i][/b][/color]

[b][size=150]Task 10[br][/size][/b][color=#ff0000]When is it possible for all four special points to be collinear? [br][b][i][size=150][size=200]>>> Record your conjecture on your handout paper.[/size][/size][/i][/b][/color]

[b][size=150]Task 11[br][/size][/b][color=#ff0000]When is it possible for all four special points to be concurrent? [br][b][i][size=150][size=200][br]>>> Record your conjecture on your handout paper.[/size][/size][/i][/b][/color]