NY-G.CO.7

GeometryCongruence60 target questions

Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.

Sample Practice Questions (3)

Triangle

A B C

has vertices

A (1, 2)

B (4, 2)

, and

C (1, 6)

. Triangle

A^{'} B^{'} C^{'}

has vertices

A^{'} (- 1, 2)

B^{'} (- 4, 2)

, and

C^{'} (- 1, 6)

. Which rigid motion maps

△ A B C

onto

△ A^{'} B^{'} C^{'}

, proving they are congruent?

AA reflection over the

y

-axis.

BA reflection over the

x

-axis.

CA translation 2 units to the left.

DA rotation of

9 0^{\circ}

counterclockwise about the origin.

Multiple choice · diagramSee Answer + Explanation →

In the coordinate plane shown below,

△ A B C

has vertices

A (1, 1)

B (4, 1)

, and

C (1, 3)

△ A^{'} B^{'} C^{'}

has vertices

A^{'} (- 1, 1)

B^{'} (- 4, 1)

, and

C^{'} (- 1, 3)

. Which rigid motion maps

△ A B C

onto

△ A^{'} B^{'} C^{'}

AA reflection over the x-axis

BA reflection over the y-axis

CA rotation of

9 0^{\circ}

clockwise about the origin

DA translation 2 units to the left

Multiple choice · diagramSee Answer + Explanation →

Triangle

R S T

is shown on the coordinate plane with vertices

R (2, 2)

S (5, 2)

, and

T (2, 4)

. If

△ R S T

is translated by the rule

(x, y) \to (x - 6, y - 2)

and then reflected over the x-axis to form

△ R^{''} S^{''} T^{''}

, what are the coordinates of

S^{''}

(- 1, 0)

(- 1, 4)

(1, 0)

(- 4, 0)

Multiple choice · diagramSee Answer + Explanation →

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More Geometry Standards

NY-G.CO.1Know precise definitions of angle circle perpendicular line parallel line and line segment based on the undefined notions of point line distance along a line and distance around a circular arc.→NY-G.CO.2Represent transformations in the plane; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not.→NY-G.CO.3Given a rectangle parallelogram trapezoid or regular polygon describe the rotations and reflections that carry it onto itself.→NY-G.CO.4Develop definitions of rotations reflections and translations in terms of angles circles perpendicular lines parallel lines and line segments.→

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