IM Geo.1.7 Lesson: Construction Techniques 5: Squares
Which one doesn’t belong?
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[/img][/td][td][img]data:image/png;base64,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[/img][/td][/tr][/table]
Use straightedge and compass tools to construct a square with segment AB as one of the sides.
Here is square ABCD with diagonal BD drawn:
[list][*]Construct a circle centered at [math]A[/math] with radius [math]AD[/math].[/*][*]Construct a circle centered at [math]C[/math] with radius [math]CD[/math].[br][/*][*]Draw the diagonal [math]AC[/math] and write a conjecture about the relationship between the diagonals[math]BD[/math] and [math]AC[/math].[br][/*][*]Label the intersection of the diagonals as point [math]E[/math] and construct a circle centered at [math]E[/math] with radius [math]EB[/math].[br][/*][/list][br]How are the diagonals related to this circle?
Use your conjecture and straightedge and compass tools to construct a square inscribed in a circle.
Use straightedge and compass moves to construct a square that fits perfectly outside the circle, so that the circle is inscribed in the square.
How do the areas of these 2 squares compare?
IM Geo.1.7 Practice: Construction Techniques 5: Squares
Which of these statements is true?
This diagram is a straightedge and compass construction of a square BACD (not all markings are shown).
[img]data:image/png;base64,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[/img][br]The construction followed these steps:[br][list][*]Start with two marked points [math]A[/math] and [math]B[/math][/*][*]Use a straightedge to construct line [math]AB[/math][br][/*][*]Use a previous construction to construct a line perpendicular to [math]AB[/math] passing through [math]A[/math][br][/*][*]Use a previous construction to construct a line perpendicular to [math]AB[/math] passing through [math]B[/math][br][/*][*]Use a compass to construct a circle centered at [math]A[/math] passing through [math]B[/math][br][/*][*]Label an intersection point of that circle and the line from step 3 as [math]C[/math][br][/*][*]Use a previous construction to construct a line parallel to [math]AB[/math] passing through [math]C[/math][br][/*][*]Label the intersection of that line and the line from step 4 as [math]D[/math][br][/*][*]Use a straightedge to construct the segments [math]AC,CD,[/math] and [math]DB[/math][br][/*][/list][br]Explain why you need to construct a circle in step 5.[br]Use the applet below if it is needed.
To construct a line passing through the point C that is parallel to the line AB, the first step is to create a line through C perpendicular to AB.
[img]data:image/png;base64,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[/img]
Jada wanted to construct a line perpendicular to line l through point C. The diagram shows her construction.
What was her mistake?
Noah is trying to bisect angle BAC. He draws circles of the same radius with centers B and C and then uses one of the points of intersection for his ray.
What mistake has Noah made in his construction?
Here is a straightedge and compass construction. Use a straightedge to draw an equilateral triangle on the figure.
Explain how you know the triangle is equilateral.
Here are 2 points in the plane.
Explain how to construct a line segment that is half the length of segment [math]AB[/math].