Geometry | Unit 1 | Lesson 19: Evidence, Angles, and Proof | Practice Problems

What is the measure of angle \(ABE\)?

• 40 degrees

• 50 degrees

• 60 degrees

• 70 degrees

• 80 degrees

Tags

CCSS.7.G.B.5

Select all true statements about the figure.

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

• Rotate 180 degrees using center \(B\). Then angle \(CBD\) is the image of angle \(EBA\).

• Reflect across the angle bisector of angle \(ABC\). Then angle \(CBD\) is the image of angle \(ABE\).

Tags

CCSS.8.G.A.3

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

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

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 \(DE\).

Tags

CCSS.8.G.A.3

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 \(D’\).

Tags

CCSS.8.G.A.2

CCSS.HSG.CO.B.6

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 \(C’\).

Tags

CCSS.8.G.A.2

CCSS.HSG.CO.B.6

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.

Tags

CCSS.HSG.GPE.B.5

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 \(BA\).

• Rotate \(60^\circ\) clockwise around point \(B\) and then translate by directed line segment \(CB\).

• Translate so that \(E\) is taken to \(H\). Then rotate \(120^\circ\) clockwise around point \(H\).

• Translate so that \(A\) is taken to \(J\). Then reflect over line \(BA\).

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5