Read the following statement: Line segment CD is congruent to line segment XY.
Which of the following is an equivalent statement? (4 points)
CD overbar is similar to XY overbar
CD overbar is congruent to XY overbar
CD overbar equals XY overbar
CD overbar is an element of XY overbar
CD overbar is congruent to XY overbar
The figure shows two triangles on a coordinate grid:
A coordinate grid is shown from positive 6 to negative 6 on the x-axis and from positive 6 to negative 6 on the y-axis. A triangle ABC is shown with vertex A on ordered pair negative 4, negative 1, vertex B on ordered pair negative 3, negative 1 and vertex C on ordered pair negative 4, negative 4. Another triangle A prime B prime C prime is shown with vertex A prime on ordered pair negative 1, 1, vertex B prime on ordered pair negative 2, 1, and vertex C prime on ordered pair negative 1, 4.
What set of transformations is performed on triangle ABC to form triangle A′B′C′? (4 points)
A translation 5 units up followed by a 180-degree counterclockwise rotation about the origin
A translation 5 units up followed by a 270-degree counterclockwise rotation about the origin
A 180-degree counterclockwise rotation about the origin followed by a translation 5 units to the left
A 270-degree counterclockwise rotation about the origin followed by a translation 5 units to the left
A translation 5 units up followed by a 270-degree counterclockwise rotation about the origin
Which statement is true about the result of a rigid transformation? (4 points)
The image will be larger than the pre-image.
The pre-image will be larger than the image.
Each one is unique; no general statement can be made about size.
The pre-image will be congruent to the image.
The pre-image will be congruent to the image.
Figure TUVW is transformed to T′U′V′W′, as shown:
A coordinate plane is shown. Figure TUVW has vertices T at 3 comma negative 4, U at 4 comma negative 2, V at 6 comma negative 1 and W at 6 comma negative 4. Figure T prime U prime V prime W prime has vertices at T prime negative 5 comma negative 4, U prime at negative 6 comma negative 2, V prime at negative 8 comma negative 1, and W prime at negative 8 comma negative 4.
Which of the following sequences of transformations is used to obtain figure T′U′V′W′ from TUVW? (4 points)
Reflection about the y-axis followed by a translation left by 2 units
Reflection about the x-axis followed by a translation left by 2 units
Counterclockwise rotation by 90 degrees about the origin followed by a translation right by 2 units
Counterclockwise rotation by 90 degrees about the origin followed by a translation left by 2 units
Counterclockwise rotation by 90 degrees about the origin followed by a translation left by 2 units
Figure QRTS is reflected about the y-axis to obtain figure Q′R′T′S′:
A coordinate plane with two quadrilaterals is shown. Figure QRTS has vertices Q at negative 5 comma 3, R at negative 5 comma 1, S at negative 2 comma 2 and T at negative 2 comma 0. Figure Q prime R prime T prime S prime has vertices Q prime at 5 comma 3, R prime at 5 comma 1, S prime at 2 comma 2 and T prime at 2 comma 0.
Which statement best describes the relationship between the two figures? (4 points)
Figure QRTS is bigger than figure Q′R′T′S′.
Figure QRTS is congruent to figure Q′R′TS′.
The measure of angle R is equal to the measure of angle Q′.
The measure of angle S is equal to the measure of angle T′.
The measure of angle R is equal to the measure of angle Q′.
To determine which statement is equivalent to the given statement "Line segment CD is congruent to line segment XY," we need to understand the meaning of the options provided.
Option 1: CD overbar is similar to XY overbar
The term "similar" indicates that two objects have the same shape but possibly different sizes. Since the original statement states that the line segments are congruent (meaning they have the same length), this option is not equivalent.
Option 2: CD overbar is congruent to XY overbar
This option uses the term "congruent," which means that two objects have the same shape and size. It matches the original statement, so it is equivalent.
Option 3: CD overbar equals XY overbar
The term "equals" indicates that two objects are exactly the same in value or measurement. Since the original statement uses the term "congruent" (for length), this option is not equivalent.
Option 4: CD overbar is an element of XY overbar
The phrase "is an element of" typically relates to set theory, expressing that one object is a member or part of another set. It does not accurately convey the relationship between the line segments, so this option is not equivalent.
Therefore, the equivalent statement to "Line segment CD is congruent to line segment XY" is: CD overbar is congruent to XY overbar.