Question

the graph shows quadrilaterals abcd and wxyz. is abcd congruent to wxyz? justify your answer. yes, because a reflection across the y - axis maps abcd onto wxyz. yes, because a translation right 10 units maps abcd onto wxyz. no, because cd and yz do not have the same length. no, because ∠b and ∠x do not have the same measure.

Explanation:

Step1: Recall congruence criteria

Congruent figures have same - shape and size, corresponding sides and angles are equal.

Step2: Analyze side - length

Use the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$ to find lengths of corresponding sides. For example, if $C(-5,2)$ and $D(-8,7)$ and $Y(5,2)$ and $Z(2,7)$.
The length of $\overline{CD}=\sqrt{(- 8+5)^2+(7 - 2)^2}=\sqrt{(-3)^2+5^2}=\sqrt{9 + 25}=\sqrt{34}$.
The length of $\overline{YZ}=\sqrt{(2 - 5)^2+(7 - 2)^2}=\sqrt{(-3)^2+5^2}=\sqrt{9+25}=\sqrt{34}$.

Step3: Analyze angle - measure

Since the figures are symmetric about the y - axis, corresponding angles are equal. A reflection across the y - axis maps quadrilateral $ABCD$ onto $WXYZ$.

Answer:

Yes, because a reflection across the y - axis maps $ABCD$ onto $WXYZ$.