IM G Unit 1 Lesson 21
Here are 2 lines [i]l[/i] and [i]m[/i] that are [i]not[/i] parallel that have been cut by a transversal.[br][br]Tyler thinks angle [i]EBF[/i] is congruent to angle [i]BCD[/i] because they are corresponding angles and a translation along the directed line segment from [i]B[/i] to [i]C[/i] would take one angle onto the other. Here are his reasons.[br][br][list][*]The translation takes [i]B[/i] onto [i]C[/i], so the image of [i]B[/i] is [i]C[/i].[/*][*]The translation takes [i]E[/i] somewhere on ray [i]CB[/i] because it would need to be translated by a distance greater than [i]BC[/i] to land on the other side of [i]C[/i].[/*][*]The image of [i]F[/i] has to land somewhere on line [i]m[/i] because translations take lines to parallel lines and line [i]l[/i] is the only line parallel to [i]l[/i] that goes through [i]B'[/i].[/*][*]The image of [i]F[/i], call it [i]F'[/i], has to land on the right side of line [i]BC[/i] or else line [i]EF'[/i] wouldn’t be parallel to the directed line segment from [i]B[/i] to [i]C[/i].[/*][/list][br]
Pick one of Tyler's statement. Is the statement true? Explain your answer.
Pick one of Tyler's statement. Is the statement true? Explain your answer.
[list=1][*]In what circumstances are corresponding angles congruent? Be prepared to share your reasoning.[/*][/list][br]
[list=1][*]In what circumstances are corresponding angles congruent? Be prepared to share your reasoning.[/*][/list][br]
Here is triangle [i]ABC [/i]with interior angles [i]a, b, and c.[br][br][/i]Points [i]D[/i] and [i]E[/i] are midpoints of sides [i]AC[/i] and [i]BC.[br][br][/i]Draw line [i]AB[/i].[br][br]Use what you know about rotations to create a line parallel to line [i]AB[/i] that goes through the opposite vertex.[br]
Triangle Angle Sum One Way
What is the value of [i]a[/i] + [i]b [/i]+ [i]c[/i]? Explain your reasoning.
Triangle Angle Sum Another Way
Draw line [i]AB[/i].[br][br]Translate triangle [i]ABC[/i] along the directed line segment from [i]B[/i] to [i]C[/i] to make triangle [i]A'B'C'[/i]. Label the angles in triangle [i]A'B'C'[/i].[br][br]Translate triangle [i]A'B'C'[/i] along the directed line segment from [i]A'[/i] to [i]C[/i] to make triangle [i]A''B''C''[/i]. Label the angles in triangle [i]A''B''C''[/i].[br][br]Label the angles that meet at point [i]C[/i]. [br][br]
What is the value of [i]a[/i] + [i]b [/i]+ [i]c[/i]? Explain your reasoning.
IM G Unit 1 Lesson 21 from IM Geometry by Illustrative Mathematics, https://im.kendallhunt.com/HS/students/2/1/21/index.html. Licensed under the Creative Commons Attribution 4.0 license, [url=https://creativecommons.org/licenses/by/4.0/]https://creativecommons.org/licenses/by/4.0/[/url].