Congruent Figures Quick Check
1 of 51 of 5 Items
Question
Use the image to answer the question.
A coordinate plane with 4 quadrants shows x and y axes ranging from negative 8 to 8 in increments of 1. Three triangles are formed by joining three plotted points each. Two of the triangles are joined by connecting their vertices with rays. The coordinates of the plotted points for the triangle in quadrant 4 are left parenthesis 1 comma negative 3 right parenthesis, left parenthesis 3 comma negative 3 right parenthesis, and left parenthesis 1 comma negative 7 right parenthesis. The coordinates for the triangle in quadrant 2 are as follows left parenthesis negative 5 comma 3 right parenthesis, left parenthesis negative 1 comma 3 right parenthesis, and left parenthesis negative 5 comma 5 right parenthesis. The side joining the vertices at left parenthesis negative 5 comma 3 right parenthesis and left parenthesis negative 5 comma 5 right parenthesis is labeled as e. The side joining the vertices at left parenthesis negative 5 comma 5 right parenthesis and left parenthesis negative 1 comma 3 right parenthesis is labeled as g. The side joining the vertices at left parenthesis negative 5 comma 3 right parenthesis and left parenthesis negative 1 comma 3 right parenthesis is labeled as h. The coordinates of the plotted points for the triangle in quadrant 1 are left parenthesis 3 comma 1 right parenthesis, left parenthesis 7 comma 1 right parenthesis, and left parenthesis 3 comma 3 right parenthesis. Three rays join the complementary vertices of the triangles in quadrants 1 and 2. A ray connects point left parenthesis 3 comma 1 right parenthesis and the point left parenthesis negative 5 comma 3 right parenthesis. A ray connects point left parenthesis 7 comma 1 right parenthesis and the point left parenthesis negative 1 comma 3 right parenthesis. A ray connects point left parenthesis 3 comma 3 right parenthesis and the point left parenthesis negative 5 comma 5 right parenthesis. The arrow heads are on the vertices of the triangle in quadrant 2.
Describe the series of transformations that have occurred to move the triangle in Quadrant IV to the triangle in Quadrant II to show that the triangles are congruent.(1 point)
Responses
translation, then rotation
translation, then rotation
rotation, then reflection
rotation, then reflection
reflection, then translation
reflection, then translation
rotation, then translation
translation, then rotation
Use the image to answer the question.
A coordinate plane with 4 quadrants shows x and y axes ranging from negative 6 to 6 in increments of 1. Three triangles are formed by joining three plotted points each. The coordinates of the plotted points for the first triangle upper A upper B upper C joined by solid lines are upper A is left parenthesis negative 4 comma 5 right parenthesis, upper B is left parenthesis negative 1 comma 3 right parenthesis, and upper C is left parenthesis negative 3 comma 1 right parenthesis. The coordinates for the second triangle upper A prime upper B prime upper C prime joined by dotted lines are as follows: upper A prime at left parenthesis 4 comma 5 right parenthesis, upper B prime at left parenthesis 1 comma 3 right parenthesis, and upper C prime at left parenthesis 3 comma 1 right parenthesis. The coordinates of the plotted points for the third triangle upper A double prime upper B double prime upper C double prime joined by lines made of dashes and dots are as follows: upper A double prime at left parenthesis 1 comma 0 right parenthesis, upper B double prime at left parenthesis negative 2 comma negative 2 right parenthesis, and upper C double prime at left parenthesis 0 comma negative 4 right parenthesis.
How would you describe this series of transformations?
(1 point)
Responses
Translation of (2,0) and then reflection across the x-axis shows that triangle ABC is congruent to triangle A′′B"C".
Translation of left parenthesis 2 comma 0 right parenthesis and then reflection across the x -axis shows that triangle upper A upper B upper C is congruent to triangle upper A double prime upper B double prime upper C double prime .
Since triangles ABC and A′′B"C" do not have the same orientation, they are not congruent.
Since triangles upper A upper B upper C and upper A double prime upper B double prime upper C double prime do not have the same orientation, they are not congruent.
Reflection across the y-axis and then a translation of (−3,−5) shows that triangle ABC is congruent to triangle A′′B"C".
Reflection across the y -axis and then a translation of left parenthesis negative 3 comma negative 5 right parenthesis shows that triangle upper A upper B upper C is congruent to triangle upper A double prime upper B double prime upper C double prime .
Rotation of 90 degrees clockwise and then reflection across the x-axis shows that triangle ABC is congruent to triangle A′′B"C".
Translation of (2,0) and then reflection across the x-axis shows that triangle ABC is congruent to triangle A′′B"C".
Use the image to answer the question.
An illustration of a coordinate plane with four quadrants shows the x and y axes extending from negative 10 to 10 in increments of 1. Three triangles are plotted on the graph. The first triangle is placed in the first quadrant with vertices marked as closed points at the following coordinates: left parenthesis 3 comma 1 right parenthesis, left parenthesis 3 comma 3 right parenthesis, and left parenthesis 7 comma 1 right parenthesis. The second triangle is placed in the second quadrant with vertices marked as closed points at the following coordinates: left parenthesis negative 1 comma 3 right parenthesis, left parenthesis negative 5 comma 3 right parenthesis, and left parenthesis negative 5 comma 5 right parenthesis. The third triangle is placed in the fourth quadrant with vertices marked as closed points at the following coordinates: left parenthesis 1 comma negative 3 right parenthesis, left parenthesis 1 comma negative 7 right parenthesis, and left parenthesis 3 comma negative 3 right parenthesis. An arrow goes from the point left parenthesis 3 comma 1 right parenthesis to left parenthesis negative 5 comma 3 right parenthesis; an arrow goes from the point left parenthesis 3 comma 3 right parenthesis to left parenthesis negative 5 comma 5 right parenthesis; an arrow goes from left parenthesis 7 comma 1 right parenthesis to left parenthesis negative 1 comma 3 right parenthesis.
Describe the sequence of steps used to move the triangle in Quadrant IV to the triangle in Quadrant II to show that the triangles are congruent.
(1 point)
Responses
translation, then transformation
translation, then transformation
translation, then reflection
translation, then reflection
reflection, then translation
reflection, then translation
rotation, then translation
rotation, then translation
translation, then reflection
Use the image to answer the question.
An illustration of a coordinate plane with four quadrants shows the x and y axes extending from negative 5 to 5 in increments of 1. Three triangles are plotted on the graph. The first triangle is placed in the first quadrant with vertices marked as closed points at the following coordinates: left parenthesis 1 comma 1 right parenthesis, left parenthesis 3 comma 1 right parenthesis, and left parenthesis 2 comma 3 right parenthesis. The second triangle is placed in the second quadrant with vertices marked as closed points at the following coordinates: left parenthesis negative 2 comma 2 right parenthesis, left parenthesis negative 3 comma 4 right parenthesis, and left parenthesis negative 4 comma 2 right parenthesis. The third triangle is placed in the fourth quadrant with vertices marked as closed points at the following coordinates: left parenthesis 1 comma negative 1 right parenthesis, left parenthesis 1 comma negative 3 right parenthesis, and left parenthesis 3 comma negative 2 right parenthesis. An arrow goes from the point left parenthesis 1 comma 1 right parenthesis to left parenthesis negative 4 comma 2 right parenthesis; an arrow goes from the point left parenthesis 2 comma 3 right parenthesis to left parenthesis negative 3 comma 4 right parenthesis; an arrow goes from left parenthesis 3 comma 1 right parenthesis to left parenthesis negative 2 comma 2 right parenthesis.
What is the sequence of steps used to move the triangle in Quadrant IV to the triangle in Quadrant II to show that the triangles are congruent?
(1 point)
Responses
translation, then transformation
translation, then transformation
rotation, then translation
rotation, then translation
translation, then reflection
translation, then reflection
reflection, then translation
reflection, then translation
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translation, then reflection
Congruent Figures Quick Check
5 of 55 of 5 Items
Question
Use the image to answer the question.
An illustration of a coordinate plane with four quadrants shows the x and y axes extending from negative 10 to 10 in increments of 1. Two triangles, upper A upper B upper C and upper E upper G upper H, are plotted on the graph. The triangle upper A upper B upper C has its vertices marked with closed points at upper A left parenthesis 1 comma negative 1 right parenthesis, upper B left parenthesis 1 comma negative 3 right parenthesis, and upper C left parenthesis 4 comma negative 3 right parenthesis. The triangle upper E upper G upper H has its vertices marked with closed points at upper E left parenthesis negative 2 comma 5 right parenthesis, upper G left parenthesis negative 2 comma 3 right parenthesis, and upper H left parenthesis negative 5 comma 3 right parenthesis. In triangle upper E upper G upper H, side upper E upper G is labeled as h, side upper G upper H is labeled as e, and side upper H upper E is labeled as g.
What is the sequence of steps used to move the triangle in Quadrant IV to the triangle in Quadrant II to show that the triangles are congruent?
(1 point)
Responses
reflection to Quadrant I, then a translation of (3, 2)
reflection to Quadrant I, then a translation of left parenthesis 3 comma 2 right parenthesis
reflection to Quadrant III, then a translation of (−1, 6)
reflection to Quadrant III, then a translation of left parenthesis negative 1 comma 6 right parenthesis
rotation 90 degrees clockwise, then a translation of (1, 6)
rotation 90 degrees clockwise, then a translation of left parenthesis 1 comma 6 right parenthesis
translation to Quadrant II, then a rotation 90 degrees counterclockwise