Question

geo.1.18 practice problems (digital)
assigned by ramon matamoros on october 7, 2025
1 practice 1
the figures are congruent.
select all the sequences of transformations that would take figure 1 to figure 2.
a translate by directed line segment ad.
b rotate 180° around point e.
c translate by directed line segment ae and reflect across ac.
d translate by directed line segment ce and rotate 90° counter - clockwise around point e.
e rotate 180° around point c, translate by directed line segment ce, and reflect across segment ef.
f reflect across segment ab, rotate clockwise by angle bfe using center f, then reflect across segment ef.

Explanation:

Step1: Analyze option A

A translation by directed line - segment \(AD\) will move Figure 1 so that point \(A\) coincides with point \(D\). But the orientation of the triangle will not be correct as there is no rotation or reflection involved to match the orientation of Figure 2. So, option A is incorrect.

Step2: Analyze option B

Rotating Figure 1 \(180^{\circ}\) around point \(E\) will not map Figure 1 to Figure 2. The position and orientation of the key - points of the triangle will not match. So, option B is incorrect.

Step3: Analyze option C

1. First, translate by directed line - segment \(AE\). This will move point \(A\) to point \(E\).
2. Then, reflecting across \(AC\) will adjust the orientation of the triangle such that Figure 1 can be mapped to Figure 2. This sequence of transformations is correct.

Step4: Analyze option D

1. Translating by directed line - segment \(CE\) moves point \(C\) to point \(E\).
2. Rotating \(90^{\circ}\) counter - clockwise around point \(E\) will not give the correct orientation of Figure 2. So, option D is incorrect.

Step5: Analyze option E

1. Rotating \(180^{\circ}\) around point \(C\) changes the orientation of Figure 1.
2. Translating by directed line - segment \(CE\) moves the rotated Figure 1.
3. Reflecting across segment \(EF\) will not map Figure 1 to Figure 2. So, option E is incorrect.

Step6: Analyze option F

1. Reflecting across segment \(AB\) changes the orientation of Figure 1.
2. Rotating clockwise by angle \(BFE\) using center \(F\) further adjusts the orientation.
3. Reflecting across segment \(EF\) will not map Figure 1 to Figure 2. So, option F is incorrect.

Answer:

C. Translate by directed line segment \(AE\) and reflect across \(AC\).