The figure shows three quadrilaterals on a coordinate grid:
A coordinate plane is shown. Figure Q is a quadrilateral with sides measuring 5 and 2. Figure S is a quadrilateral with sides measuring 5 and 2. Figure W is a quadrilateral with sides measuring 10 and 4.
Which of the following statements is true about the three quadrilaterals? (4 points)
Q and W are similar but not congruent.
W and S are similar and congruent.
W and Q are similar and congruent.
Q and S are similar but not congruent.
Q and S are similar but not congruent.
To determine which statement is true, let's compare the given measurements of the sides of each quadrilateral:
- Quadrilateral Q has sides measuring 5 and 2.
- Quadrilateral S has sides measuring 5 and 2.
- Quadrilateral W has sides measuring 10 and 4.
Similar figures have corresponding sides that are proportional, and congruent figures have corresponding sides that are equal in length.
Comparing Q and W:
The sides of Q do not have the same length as the sides of W, so Q and W are not congruent.
However, since the sides of W are twice the length of the corresponding sides of Q, Q and W are similar.
Comparing S and W:
The sides of S have the same length as the sides of W, so S and W are congruent.
Additionally, since the sides of W are twice the length of the corresponding sides of S, S and W are similar.
Comparing Q and S:
The sides of Q and S have the same length, so Q and S are congruent.
However, since the sides of Q and S are not proportional, Q and S are not similar.
Therefore, the true statement is:
W and S are similar and congruent.
To determine the relationships between the three quadrilaterals (Q, S, and W), we need to understand the concepts of similarity and congruence.
Two shapes are considered similar if their corresponding angles are congruent and the ratios of their corresponding side lengths are equal. Similar shapes have the same shape but can be different in size.
On the other hand, two shapes are congruent if they have the exact same shape and size. Congruent shapes have the same angles and side lengths.
Let's analyze the given information about the side lengths of each quadrilateral:
- Quadrilateral Q has sides measuring 5 and 2.
- Quadrilateral S has sides measuring 5 and 2.
- Quadrilateral W has sides measuring 10 and 4.
Now, let's compare the side lengths of these quadrilaterals:
- Quadrilaterals Q and S both have sides measuring 5 and 2. This indicates that they are similar in shape.
- Quadrilaterals Q and W do not have the same side lengths, so they cannot be congruent.
- Quadrilaterals S and W also do not have the same side lengths, so they cannot be congruent either.
From the information provided, the only true statement is:
Q and S are similar but not congruent. (Option: Q and S are similar but not congruent.)
To summarize, we determined the relationships between the quadrilaterals by comparing their side lengths. Quadrilaterals Q and S have the same side lengths and are similar, while quadrilaterals W and Q/S do not share the same side lengths, so they cannot be congruent.
Figure ABCD is reflected about the y-axis to obtain figure A′B′C′D′:
A coordinate plane is shown. Figure ABCD has vertices A at 2 comma 5, B at 1 comma 2, C at 3 comma 1, and D at 4 comma 5. Figure A prime B prime C prime D prime has vertices A prime at negative 2 comma 5, B prime at negative 1 comma 2, C prime at negative 3 comma 1, and D prime at negative 4 comma 5.
Which statement best describes the relationship between the two figures? (4 points)
Figure ABCD is similar to figure A′B′C′D′.
Figure ABCD is bigger than figure A′B′C′D′.
The measure of angle D is equal to the measure of angle A′.
The measure of angle D is equal to the measure of angle B′.
3.
(02.05)
Which sequence of transformations creates a similar, but not congruent, triangle? (4 points)
Rotation and translation
Dilation and rotation
Reflection and rotation
Translation and reflection
The statement that best describes the relationship between the two figures (ABCD and A'B'C'D') is:
Figure ABCD is reflected about the y-axis to obtain figure A′B′C′D′.
Regarding the sequence of transformations that creates a similar, but not congruent, triangle, the correct answer is:
Dilation and rotation.