IM Geo.6.17 Lesson: Lines in Triangles

If you have tracing paper, draw a triangle on it. Fold the altitude from each vertex. If not, observe the applet below.
Triangle ABC is graphed.
Find the slope of each side of the triangle.[br]
Find the slope of each altitude of the triangle.[br]
[list][*]Sketch the altitudes. [/*][*]Label the point of intersection [math]H[/math].[br][/*][/list][br]Write equations for all 3 altitudes.[br]
Use the equations to find the coordinates of [math]H[/math] and verify algebraically that the altitudes all intersect at [math]H[/math].[br]
[size=150]Any triangle [math]ABC[/math] can be translated, rotated, and dilated so that the image [math]A'[/math] lies on the origin, [math]B'[/math] lies on the point [math]\left(1,0\right)[/math], and [math]C'[/math] has position [math]\left(a,b\right)[/math].[/size][br][br]Use this as a starting point to prove that the altitudes of all triangles all meet at the same point.
Triangle ABC is graphed.
Find the midpoint of each side of the triangle.[br]
[list][*]Sketch the perpendicular bisectors, using the Midpoint and Perpendicular Line tools. [/*][*]Label the intersection point [math]P[/math].[br][/*][/list]Write equations for all 3 perpendicular bisectors.[br][br]
Use the equations to find the coordinates of [math]P[/math] and verify algebraically that the perpendicular bisectors all intersect at [math]P[/math].[br]
Consider triangle ABC from an earlier activity.
What is the distance from [math]A[/math] to [math]P[/math], the intersection point of the perpendicular bisectors of the triangle’s sides? Round to the nearest tenth.[br]
Write the equation of a circle with center [math]P[/math] and radius [math]AP[/math].[br]
[list][*]Construct the circle. [/*][/list][br]What do you notice?[br]
Verify your hypothesis algebraically.[br]
Consider triangle ABC from earlier activities.
[list][*]Plot point [math]H[/math], the intersection point of the altitudes.[br][/*][*]Plot point [math]P[/math], the intersection point of the perpendicular bisectors.[br][/*][*]Find the point where the 3 medians of the triangle intersect. Plot this point and label it [math]J[/math].[br][/*][/list][br]What seems to be true about points [math]H[/math], [math]P[/math], and [math]J[/math]?
Prove that your observation is true.[br]
A tessellation covers the entire plane with shapes that do not overlap or leave gaps.
[size=150]Tile the plane with congruent rectangles:[/size][br][br]Draw the rectangles on your grid.[br]
Write the equations for lines that outline 1 rectangle.[br]
[size=150]Tile the plane with congruent right triangles:[/size][br][br]Draw the right triangles on your grid.[br]
Write the equations for lines that outline 1 right triangle.[br]
[size=150]Tile the plane with any other shapes:[/size][br][br]Draw the shapes on your grid.[br]
Write the equations for lines that outline 1 of the shapes.[br]

IM Geo.6.17 Practice: Lines in Triangles

[size=150]The 3 lines [math]x=3[/math], [math]y-2.5=-\frac{1}{5}\left(x-0.5\right)[/math], and [math]y-2.5=x-3.5[/math] intersect at point [math]P[/math].[/size][br][br]Find the coordinates of [math]P[/math]. Verify algebraically that the lines all intersect at [math]P[/math].
[size=150]Triangle [math]ABC[/math] has vertices at [math]\left(0,0\right)[/math], [math]\left(5,5\right)[/math], and [math]\left(10,1\right)[/math]. Kiran calculates the point of intersection of the medians using the following steps:[br][/size][br][list=1][*]Draw the triangle.[/*][*]Calculate the midpoint of each side.[/*][*]Draw the medians.[/*][*]Write an equation for 2 of the medians.[/*][*]Solve the system of equations.[/*][/list][br]Use Kiran’s method to calculate the point of intersection of the medians.
Triangle ABC and its medians are shown.
[img]data:image/png;base64,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[/img][br][br]Write an equation for median [math]AE[/math].
[size=150]Given [math]A=\left(1,2\right)[/math] and [math]B=\left(7,14\right)[/math], find the point that partitions segment [math]AB[/math] in a [math]2:1[/math] ratio.[/size]
[size=150]A quadrilateral has vertices [math]A=\left(0,0\right)[/math], [math]B=\left(4,6\right)[/math], [math]C=\left(0,12\right)[/math], and [math]D=\left(-4,6\right)[/math].[br]Mai thinks the quadrilateral is a rhombus and Elena thinks the quadrilateral is a square.[/size][br][br]Do you agree with either of them? Show or explain your reasoning.  
[size=150]The image shows a graph of the parabola with focus [math]\left(-3,-2\right)[/math] and directrix [math]y=2[/math], and the line given by [math]y=-3[/math].[/size][br][br][img]data:image/png;base64,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[/img][br][br]Find and verify the points where the parabola and the line intersect.
[img]data:image/png;base64,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[/img][br][br][size=150]For each equation, is the graph of the equation parallel to the line shown, perpendicular to the line shown, or neither?[/size][br][br][math]y=0.25x[/math]
[math]y=2x-4[/math]
[math]y-2=-4\left(x-3\right)[/math]
[math]2y+8x=7[/math]
[math]x-4y=3[/math]
[size=150]Write 2 equivalent equations for a line with [math]x[/math]-intercept [math]\left(3,0\right)[/math] and [math]y[/math]-intercept [math]\left(0,2\right)[/math]. [/size]
[size=150]Parabola A and parabola B both have the line [math]y=-2[/math] as the directrix. Parabola A has its focus at [math]\left(3,4\right)[/math] and parabola B has its focus at [math]\left(5,0\right)[/math].[/size][size=150]Select [b]all[/b] true statements.[/size]

Information