Similarly, to find measures of vertical angles students may use a \(180^\circ\) rotation like they did earlier in this unit when showing that vertical angles are congruent. They might try to translate \(B\) to \(E\) in the third picture and observe that the angles at those two vertices are not congruent. For example, they may use tracing paper to translate vertex \(B\) to vertex \(E\). To find the measures of corresponding and alternate interior, students may use tracing paper and some of the strategies found earlier in the unit. Make sure to leave enough time for the next activity, “Alternate Interior Angles are Congruent.”Īs students work with their partners, they begin to fill in supplementary angles and vertical angles. The last two questions in this activity are optional, to be completed if time allows. They also consider whether the relationships they found hold true for any two lines cut by a transversal. Students investigate whether knowing the measure of one angle is sufficient to figure out all the angle measures in this situation. *Alternate exterior angles – congruent angles outside parallels but on opposite sides of the transversal.In this task, students explore the relationship between angles formed when two parallel lines are cut by a transversal line. *Alternate interior angles – congruent angles between parallels but on opposite sides of the transversal. Vertical angles – congruent angles across from each other when two lines, segments or rays intersect.Ĭorresponding angles – congruent angles in the same location on different parallel lines intersected by a transversal. Supplementary angles – two or more angles that add to 180 0.Ĭomplementary angles – two or more angles that add to 90 o. Transversal – a lines, segment or ray that intersects parallels. Perpendicular – lines, segments or rays that intersect at 90 o angles. They never get closer together or farther apart. Parallel – two or more lines, segments or rays that do not and would not (if extended) ever intersect. is to point out one particular figure, line, angle, etc.Ĭlassifying tells the type of geometric figure. Here are some patterns we noticed when rotating around the origin (0,0)ĭilations - point of dilation and scale factor are needed. Rotations - point of rotation (the point you rotate the figure around), number of degrees rotated, and direction of rotation are needed. Here are some examples of other lines that you could reflect across. The axes are common reflection lines, but any line is possible. Reflections - line of reflection needed (the line you reflect across). Translations - direction and number of "spaces" needed. Example: Triangle ABC has been enlarged by a scale factor of 2 to form Triangle MNP and has been shrunk by a scale factor of 0.25 to form triangle WXY The image is usually not congruent to the original. is enlarged or shrunk proportionally (looks the same, only larger or smaller) from a point. Example: Triangle ABC has been reflected across the line segment shown.ĭilation - when a shape, angle, line, etc. The image stays congruent to the original. is flipped across a line to form a mirrored image. Reflection - when a shape, angle, line, etc. Example: Triangle ABC (from above) has been rotated about 90 o clockwise to form image triangle A’B’C’. The point can be in the figure or outside of it. is turned around a point a certain number of degrees. Rotation - when a shape, angle, line, etc. The image stays congruent to the original.Įxample: Triangle ABC has been translated right and down (as seen in image DEF) Translation – when a shape, angle, line, etc. Image – the resulting figure after an original figure is transformed in some way. Congruent – exactly the same size and shape.
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