[b]a. [/b] Translate triangle [i]ABC[/i] along the vector that takes [i]A[/i] to [i]D[/i]. [br] *Select the vector tool [icon]/images/ggb/toolbar/mode_vector.png[/icon] and draw a vector starting at point [i]A[/i] and ending at point [i]D[/i]. Then, select the translate by vector tool [icon]/images/ggb/toolbar/mode_translatebyvector.png[/icon], click on triangle [i]ABC[/i], and then click on the vector.[br][br][b]b. [/b] Reflect triangle [i]ABC[/i] over line [i]m[/i].[br] *Select the reflect about line tool [icon]/images/ggb/toolbar/mode_mirroratline.png[/icon], click on triangle [i]ABC[/i], then select line [i]m[/i]. [br][br][b]c.[/b] Rotate triangle [i]ABC[/i] 70 degrees clockwise around point [i]G.[br][/i] [i]*[/i]Select the rotate around point tool [icon]/images/ggb/toolbar/mode_rotatebyangle.png[/icon], click on triangle [i]ABC[/i], then click on point [i]P[/i]. Type in 70 degrees and make sure clockwise is selected.[br][br]*If you use the move tool [icon]/images/ggb/toolbar/mode_move.png[/icon], note how you can change things dynamically. As an example, select one of the points on your line of reflection, and observe what happens.

[b]a. [/b] Measure the distance of segment [i]AB[/i]. Select the distance measuring tool [icon]/images/ggb/toolbar/mode_distance.png[/icon], then select point [i]A  [/i]followed by point [i]B[/i]. Note that if you grab the move tool [icon]/images/ggb/toolbar/mode_move.png[/icon], you can drag the label to a new location.[br][br][b]b.[/b] Repeat the process above to measure segment [i]CE[/i] and segment [i]ED. [/i]

[b]a. [/b] Measure angle [i]ABC[/i]. [br] *Select the angle measure tool [icon]/images/ggb/toolbar/mode_angle.png[/icon], then select points [i]A[/i], [i]B[/i], and [i]C[/i] in that order. Note that you must select points clockwise in GeoGebra to get the angles measured correctly. [br][br][b]b.[/b] Measure all four angles formed by the pair of intersecting lines.

[b]a. [/b] Translate triangle [i]ABC[/i] along the vector that takes [i]B[/i] to [i]G[/i]. [br] **Select the vector tool [icon]https://www.geogebra.org/images/ggb/toolbar/mode_vector.png[/icon] and draw a vector starting at point [i]B[/i] and ending at point [i]G[/i]. Then, select the translate by vector tool [icon]https://www.geogebra.org/images/ggb/toolbar/mode_translatebyvector.png[/icon], click on triangle [i]ABC[/i], and then click on the vector.[br][br][b]b. [/b] Draw another vector from point [i]A[/i] to A'[i], [/i]and from [i]C [/i]to [i]C'[/i]. You should now have three sets of vectors, each connecting a pair of corresponding points. Measure the distance of each vector by using the distance measuring tool [icon]/images/ggb/toolbar/mode_distance.png[/icon], and selecting each pair of corresponding points (as an example, click on [i]A[/i] followed by [i]A'[/i] with the tool selected).

[b]a. [/b]Reflect quadrilateral [i]ABCD[/i] over line [i]v. [br] *[/i]Select the reflect about line tool [icon]https://www.geogebra.org/images/ggb/toolbar/mode_mirroratline.png[/icon], click on quadrilateral [i]ABCD[/i], then select line [i]v[/i]. [br][b]b. [/b]Pick two pairs of corresponding points, say [i]B[/i] and [i]B'[/i], and [i]C[/i] and [i]C' [/i]and draw a line segment [icon]/images/ggb/toolbar/mode_segment.png[/icon] between them. Select the point tool [icon]/images/ggb/toolbar/mode_complexnumber.png[/icon], and mark each intersection point formed between the line of reflection and your lines connecting your corresponding points. [br][br][br][b]c.[/b] Measure the distance from the line of reflection to each pair of corresponding points using the distance tool [icon]/images/ggb/toolbar/mode_distance.png[/icon]. As an example, you are measuring the distance from the line of reflection to [i]B[/i] and the distance from the line of reflection to [i]B'. [/i] [br][br][b]d. [/b]Pick one of your lines connecting a pair of corresponding points, and measure the angle formed between that line and your line of reflection using the angle measure tool [icon]/images/ggb/toolbar/mode_angle.png[/icon]. [br]

[b]a. [/b] Rotate triangle [i]ABC[/i] around point [i]P[/i] with an angle measure and direction of your choosing. Keep your angle measures less or equal to 90 degrees. [br][br] *[i]*[/i]Select the rotate around point tool [icon]https://www.geogebra.org/images/ggb/toolbar/mode_rotatebyangle.png[/icon], click on triangle [i]ABC[/i], then click on point [i]P[/i]. Type in an angle measure of your choosing, and select either clockwise or counterclockwise. [br][br][b]b. [/b] Draw a line segment from [i]C[/i] to point [i]P[/i]. Then, draw a line segment from [i]C[/i]' to[i] P. *[/i]You can use any pair of corresponding points, it does not have to be [i]C[/i] and [i]C'[/i].[i] [br][br][/i][b]c.[/b]Measure the angle formed using the angle measuring tool [icon]/images/ggb/toolbar/mode_angle.png[/icon]. *Select your points in a clockwise order. [br][br][b]d. [/b] Measure the distance from [i]P[/i] to your two corresponding points using the distance tool [icon]/images/ggb/toolbar/mode_distance.png[/icon]. [br][br]

[b]a. [/b] Reflect triangle [i]DEF [/i]over the [i]y[/i]-axis. Then, reflect triangle [i]D'E'F' [/i]over the [i]x[/i]-axis. [br][br][b]b.[/b] Reset your image, then select triangle [i]DEF[/i] and rotate 180 degrees around point [i]P. [/i]

[b]a.[/b] Reflect triangle [i]ABC[/i] over line [i]m[/i], then reflect triangle [i]A'B'C' [/i]over line [i]n.[/i] [br][br][b]b.[/b] Measure the angle formed by drawing a line segment connecting [i]A[/i] to [i]P[/i], and [i]A''[/i] to [i]P. [/i]Write this measurement down. [br][br][b]c.[/b] Now, rotate triangle [i]ABC[/i] counterclockwise around [i]P[/i] at an angle equal to the angle you just measured in step b.