Illustrative Mathematics - Geometry - Mathematics - Unit 1 - Lesson 19 - Formative Library | Library

What is the measure of angle ABE?

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Select all true statements about the figure.

c + b = d + c

Rotate 180 degrees using center B. Then angle CBD is the image of angle EBA.

Reflect across line CE. Then angle CBD is the image of angle EBA.

Rotate clockwise by angle ABC using center B. Then angle CBD is the image of angle ABE.

d + b = 180

Reflect across the angle bisector of angle ABC. Then angle CBD is the image of angle ABE.

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Point D is rotated 180 degrees using B as the center. Explain why the image of D must lie on the ray BA.

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Draw the result of this sequence of transformations.

Rotate ABCD clockwise by angle ADC using point D as the center.
Translate the image by the directed line segment DE.

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Quadrilateral ABCD is congruent to quadrilateral A'B'C'D'. Describe a sequence of rigid motions that takes A to A', B to B', C to C', and D to D'.

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Triangle ABC is congruent to triangle A'B'C'. Describe a sequence of rigid motions that takes A to A', B to B', and C to C'.

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In quadrilateral BADC, AB = AD and BC = DC. The line AC is a line of symmetry for this quadrilateral.
Based on the line of symmetry, explain why the diagonals AC and BD are perpendicular.
Based on the line of symmetry, explain why angles ACB and ACD have the same measure.

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Here are 2 polygons:
Select all sequences of translations, rotations, and reflections below that would take polygon P to polygon Q.

Reflect over line BA and then translate by directed line segment CB.

Translate by directed line segment BA then reflect over line BA.

Translate so that A is taken to J. Then reflect over line BA.

Rotate 60° clockwise around point B and then translate by directed line segment CB.

Translate so that E is taken to H. Then rotate 120° clockwise around point H.

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This lesson is from Illustrative Mathematics. Geometry, Unit 1, Lesson 19. Internet. Available from https://curriculum.illustrativemathematics.org/HS/teachers/2/1/19/index.html ; accessed 29/July/2021.

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