Question

Figure $LMNO$ maps to $L’M’N’O’$ by a ${125}^{\circ }$ rotation about point $T$

Which congruency statement is correct?

• A. $\mathrm{LMNO}\cong \mathrm{L}\text{'}\mathrm{M}\text{'}\mathrm{N}\text{'}\mathrm{O}$
• B. $LMNO\cong O\text{'}M\text{'}N\text{'}L\text{'}$
• C. $\mathrm{ONML}\cong \mathrm{M}\text{'}\mathrm{O}\text{'}\mathrm{N}\text{'}\mathrm{L}\text{'}$
• D. $\mathrm{ONML}=\mathrm{O}\text{'}\mathrm{M}\text{'}\mathrm{N}\text{'}\mathrm{L}\text{'}$

Answer 1

The correct option is A

$\mathrm{LMNO}\cong \mathrm{L}\text{'}\mathrm{M}\text{'}\mathrm{N}\text{'}\mathrm{O}$

The explanation for the correct option:

Option(A)

Since we know that rotations are isometric and they preserve angle measures.

We can see that after rotating figure $\mathrm{LMNO}$ about point $T$, the angle $L$ will correspond to angle $L\text{'}$and angle $\mathrm{M},\mathrm{N}\mathrm{and}\mathrm{O}$ will correspond to angles $\mathrm{M}\text{'},\mathrm{N}\text{'}\mathrm{and}\mathrm{O}\text{'}$respectively.

Hence, figure $LMNO$ will be congruent to $L\text{'}M\text{'}N\text{'}O\text{'}$, option $\left(A\right)$ is correct option.

The explanation for the incorrect options:

Option(B)

Since we know that rotations are isometric and they preserve angle measures.

We can see that after rotating figure $\mathrm{LMNO}$ about point $T$, the angle $L$ will correspond to angle $L\text{'}$and angle $\mathrm{M},\mathrm{N}\mathrm{and}\mathrm{O}$ will correspond to angles $\mathrm{M}\text{'},\mathrm{N}\text{'}\mathrm{and}\mathrm{O}\text{'}$respectively.

Hence, the option $\left(B\right)$ is incorrect.

Option(C)

Since we know that rotations are isometric and they preserve angle measures.

We can see that after rotating figure $\mathrm{LMNO}$ about point T, the angle $L$ will correspond to angle $L\text{'}$and angle $\mathrm{M},\mathrm{N}\mathrm{and}\mathrm{O}$ will correspond to angles $\mathrm{M}\text{'},\mathrm{N}\text{'}\mathrm{and}\mathrm{O}\text{'}$respectively.

Hence, the option $\left(C\right)$ is incorrect.

Option(D)

Since we know that rotations are isometric and they preserve angle measures.

We can see that after rotating figure $\mathrm{LMNO}$ about point T, the angle $L$ will correspond to angle $L\text{'}$and angle $\mathrm{M},\mathrm{N}\mathrm{and}\mathrm{O}$ will correspond to angles $\mathrm{M}\text{'},\mathrm{N}\text{'}\mathrm{and}\mathrm{O}\text{'}$respectively.

Hence, the option $\left(D\right)$ is incorrect.