Rigid Transformations
These are the three primary types of rigid transformations.
What are translations, reflections, and rotations?
If triangle ABC is congruent to triangle XYZ, this side corresponds to side BC.
What is side YZ?
This tool is used in constructions to ensure that all points on a curve are the same distance from a center point.
Hint: This tool helped us create PERFECT circles!
What is a compass?
A square has this many lines of symmetry.
What is four?
When two parallel lines are cut by a transversal, these angles are on opposite sides of the transversal and inside the parallel lines.
What are Alternate Interior Angles?
Rigid transformations are "rigid" because they preserve these two properties of a figure.
What are distance/length and angle measures?
This is the vocab term for parts of congruent figures that "match up."
What are corresponding parts?
When constructing an equilateral triangle, we use two circles with the same radius. The third vertex of the triangle is located here.
What is the intersection of the two circles?
This type of symmetry exists when a figure can be mapped onto itself by a rotation of less than 360 degrees.
What is rotational symmetry?
This theorem states that when two lines intersect, the angles opposite each other are congruent.
What is the Vertical Angles Theorem?
If you translate a point (x, y) by the vector <3, -2>, this is the new coordinate. 2x**Double Jeopardy**2x
Reminder: -5 on the x-axis would be x-5,
-5 on the y-axis would be y-5
(x-5,y-5)
What is (x+3, y-2)?
Write a congruence statement for two rectangles, ABCD and EFGH, where A maps to E and B maps to F.
What is ABCD is congruent to EFGH?
To construct a perpendicular bisector of segment AB, you must draw two circles with this specific requirement for their radii.
2x**DOUBLE JEOPARDY**2x
What is equal radii?
Describe a sequence of two transformations that would take a figure in Quadrant I to its mirror image in Quadrant III.
What is a reflection over the x-axis followed by a reflection over the y-axis?
or
What is a 180 degree rotation?
If you know that alternate interior angles are congruent, you can conclude this about the two lines.
What is that the lines are parallel?
To perform a rotation, you must specify these three things.
What are the center of rotation, the angle of rotation, and the direction/clockwise or counter-clockwise?
To justify that two figures are congruent, you must describe a sequence of these that maps one onto the other.
What are rigid transformations?
Or
(What are translations, rotations, and reflections?)
To construct a regular hexagon inscribed in a circle, you first place your compass point on the circle to draw an arc. To find the next vertex, you must keep your compass at the exact same width as this specific part of the circle. What part of the circle determines that width?
What is the radius?
To take a regular hexagon onto itself, you could rotate it about its center by any multiple of this many degrees.
Hint: The answer is in the back of your book.
What is a 60 degree rotation?
Before writing a proof, we do this to a diagram to keep track of given information and congruent parts.
What is labeling or marking the diagram?
True or False: A sequence of a reflection followed by a translation results in a figure that is NOT congruent to the original.
What is False?
If triangle PQR is reflected across the x-axis to create triangle P'Q'R', name the angle in the image that is congruent to angle Q.
What is angle Q'?
In geometry constructions, we don't use rulers to measure inches or centimeters. Instead, we use a compass to draw circles or arcs. Why is a circle the perfect tool to use when we need to create two line segments that are exactly the same length?
What is because all radii of the same circle are equal?
If you reflect a figure over line m and then reflect it over line n (where $m$ and $n$ are parallel), the result is equivalent to this single transformation.
2x**DOUBLE JEOPARDY**2X
What is a translation?
Provide a conjecture about the sum of the interior angles of a triangle.
Hint: What is true of all triangles and the sum of their angles?
What is "The sum of the interior angles of any triangle is 180"?