IM Geo.1.12 Lesson: Defining Translations
What do you notice? What do you wonder?
[img]data:image/png;base64,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[/img]
After a translation, the image of V is W.
Find at least 3 other points that are taken to a labeled point by that translation.[br]
Write at least 1 conjecture about translations.
In a new translation, the image of V is Z.
Find at least 3 other points that are taken to a labeled point by the new translation.
Are your conjectures still true for the new translation?[br]
[size=150]Translate triangle [math]ABC[/math] by [b]the directed line segment[/b] from[math]A[/math] to [math]C[/math].[/size][br][br]What is the relationship between line [math]BC[/math] and line [math]B'C'[/math]? Explain your reasoning.[br]
How does the length of segment [math]BC[/math] compare to the length of segment [math]B'C[/math]'? Explain your reasoning.[br]
[size=150]Translate segment [math]DE[/math] by directed line segment w. Label the new endpoints [math]D'[/math] and [math]E'[/math].[/size][br][br]Connect [math]D[/math] to [math]D'[/math] and [math]E[/math] to [math]E'.[/math][br]What kind of shape did you draw? Explain your reasoning.[br]
What properties does it have? Explain your reasoning.
On triangle [math]ABC[/math] in the task, use a straightedge and compass to construct the line which passes through [math]A[/math] and is perpendicular to [math]AC[/math]. Label it [math]l[/math]. Then, construct the perpendicular bisector of [math]AC[/math] and label it [math]m[/math]. Draw the reflection of [math]ABC[/math] across the line [math]l[/math]. Since the label [math]A'B'C'[/math] is used already, label it [math]DEF[/math] instead. [br][br]What is the reflection of [math]DEF[/math] across the line [math]m[/math]?[br]
Explain why this is cool.[br]
IM Geo.1.12 Practice: Defining Translations
Match the directed line segment with the image of Polygon P being transformed to Polygon Q by translation by that directed line segment.
Draw the image of quadrilateral ABCD when translated by the directed line segment v. Label the image of A as A', the image of B as B', the image of C as C' and the image of D as D'.
[size=150]Which statement is true about a translation?[/size]
[size=150]Select all the points that stay in the same location after being reflected across line [math]l[/math].[br][img]data:image/png;base64,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[/img][/size]
[size=150]Lines[math]l[/math] and [math]m[/math] are perpendicular. A point [math]Q[/math] has this property: rotating [math]Q[/math] 180 degrees using center [math]P[/math] has the same effect as reflecting [math]Q[/math] over line [math]m[/math]. Give two possible locations of [math]Q[/math].[/size]
Do all points in the plane have this property?[br]
There is a sequence of rigid transformations that takes A to A'. B to B', and C to C'. The same sequence takes D to D'. Draw and label D'
[size=150]Two distinct lines, [math]l[/math] and [math]m[/math], are each perpendicular to the same line [math]n[/math]. [/size][br][br]What is the measure of the angle where line [math]l[/math] meets line [math]n[/math]?[br]
What is the measure of the angle where line [math]m[/math] meets line [math]n[/math]?[br]