Question

describe a congruence transformation that maps △abc onto △efg. complete the statement: △abc rotates ________ about the origin, followed by a translation ______. lesson 4.4 practice exercise #4 describe a congruence transformation that maps pqrs onto wxyz. complete the statement: pqrs reflects in the ______, followed by a reflection ________. lesson 4.4 practice exercise #1 consider the figures graphed below. identify any congruent figures in the coordinate plane. select all that apply. a. △qrs≅△hjk b. △tuv≅△hjk c. mnpl≅ defg d. △abc≅△tuv e. △abc≅△hjk f. fgde≅ nplm

Explanation:

1. For $\triangle ABC$ and $\triangle EFG$:

• Observe the orientation change. $\triangle ABC$ rotates $180^{\circ}$ counter - clockwise (or clockwise, since a $180^{\circ}$ rotation is the same in either direction) about the origin. To find the translation, compare the position of a vertex of the rotated triangle to the corresponding vertex of $\triangle EFG$. After rotating $\triangle ABC$ $180^{\circ}$ about the origin, we translate it $1$ unit down.

2. For $\square PQRS$ and $\square WXYZ$:

• First, $\square PQRS$ reflects in the $y$ - axis. Then, to map it onto $\square WXYZ$, it reflects in the $x$ - axis.

3. For identifying congruent figures:

• Congruent figures have the same shape and size. By counting the side - lengths and checking the angles (since on a grid, right - angled figures' side - lengths can be easily compared), we find that:
• $\triangle ABC\cong\triangle HJK$ as they have the same side - lengths and shape.
• $\square MNPL\cong\square DEFG$ as they have the same side - lengths and shape.
• $\square FGDE\cong\square NPLM$ as they are just different orientations of the same - sized rectangle.

Answer:

1. $\triangle ABC$ rotates $180^{\circ}$ about the origin, followed by a translation $1$ unit down.
2. $\square PQRS$ reflects in the $y$ - axis, followed by a reflection in the $x$ - axis.
3. C. $\square MNPL\cong\square DEFG$

E. $\triangle ABC\cong\triangle HJK$
F. $\square FGDE\cong\square NPLM$