lesson 3 practice problems
1. triangle abc is congruent to triangle edf. so, kiran knows that there is a sequence
of rigid motions that takes abc to edf.
select all true statements after the transformations:
a. angle a coincides with angle f.
b. angle b coincides with angle d.
c. segment ac coincides with segment ef.
d. segment bc coincides with segment ed.
e. segment ab coincides with segment ed.
2. a rotation by angle ace using point c as
the center takes triangle cba onto
triangle cde.
a. explain why the image of ray ca lines up with ray ce.
b. explain why the image of a coincides with e.
c. is triangle cba congruent to triangle cde? explain your reasoning.

Question

Accepted Answer

1.
# Explanation:
## Step1: Analyze congruent triangles
Since $\triangle ABC\cong\triangle EDF$, corresponding parts are equal. Corresponding angles: $\angle A=\angle E$, $\angle B = \angle D$, $\angle C=\angle F$. Corresponding sides: $AB = ED$, $BC=DF$, $AC=EF$

## Step2: Check each option
- Option A: $\angle A$ corresponds to $\angle E$, not $\angle F$. So, A is false.
- Option B: $\angle B$ corresponds to $\angle D$. So, B is true.
- Option C: $AC$ corresponds to $EF$. So, C is true.
- Option D: $BC$ corresponds to $DF$, not $ED$. So, D is false.
- Option E: $AB$ corresponds to $ED$. So, E is true.

# Answer:
B. Angle $B$ coincides with angle $D$, C. Segment $AC$ coincides with segment $EF$, E. Segment $AB$ coincides with segment $ED$

2.
a.
# Brief Explanations:
A rotation about point $C$ by angle $ACE$ means that the measure of the angle between $CA$ and $CE$ is the angle of rotation. When we rotate ray $CA$ around point $C$ by angle $ACE$, it will land on ray $CE$ because the rotation is defined by the angle between $CA$ and $CE$ with center $C$.

# Answer:
The rotation is by the angle $ACE$ with center $C$, so ray $CA$ rotates to ray $CE$

b.
# Brief Explanations:
Since the rotation is about point $C$ (a rigid - motion), and $CA = CE$ (because in a rotation, the distance from the center of rotation to a point and its image is the same). Also, as we saw in part (a) ray $CA$ maps to ray $CE$. So, the point $A$ (which is on ray $CA$ at a distance $CA$ from $C$) maps to point $E$ (which is on ray $CE$ at a distance $CE = CA$ from $C$)

# Answer:
$CA=CE$ (rotation preserves distance) and ray $CA$ maps to ray $CE$ (rotation by $\angle ACE$), so $A$ maps to $E$

c.
# Brief Explanations:
A rotation is a rigid motion. Rigid motions (rotations, translations, reflections) preserve side - lengths and angle - measures. So, if we can map $\triangle CBA$ to $\triangle CDE$ using a rotation (a rigid motion), then all corresponding sides and angles of $\triangle CBA$ and $\triangle CDE$ are equal. By the definition of congruent triangles (if there is a rigid motion that maps one triangle to another, the two triangles are congruent)

# Answer:
Yes, because a rotation (a rigid motion) maps $\triangle CBA$ to $\triangle CDE$, and rigid motions preserve side - lengths and angle - measures.

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QUESTION IMAGE

Question

Explanation:

Step1: Analyze congruent triangles

Step2: Check each option

Answer: