To address the problem in the image, I'll help you step by step:

Part (a): Finding missing angles in the triangles

In $\triangle ABC$ and $\triangle DEF$:

• Given $m\angle A = 22^\circ$, $m\angle B = 50^\circ$, and $m\angle D = 22^\circ$, $m\angle E = 50^\circ$.

• Use the angle sum property of triangles ($m\angle A + m\angle B + m\angle C = 180^\circ$) to find the missing angles:

  For $\triangle ABC$:
  $m\angle C = 180^\circ - (22^\circ + 50^\circ) = 108^\circ.$

  For $\triangle DEF$:
  $m\angle F = 180^\circ - (22^\circ + 50^\circ) = 108^\circ.$

Thus: $m\angle C = 108^\circ, \quad m\angle F = 108^\circ.$

Part (b): Measuring the side lengths

You need to use a ruler to measure the side lengths of each triangle. Measure and input the following lengths in whole numbers:

• For $\triangle ABC$: $AB$, $BC$, $CA$.
• For $\triangle DEF$: $DE$, $EF$, $FD$.

Part (c): Finding the ratios of corresponding side lengths

Using the side lengths from part (b), calculate these ratios and simplify them: $\frac{AB}{DE}, \quad \frac{BC}{EF}, \quad \frac{CA}{FD}.$

Simplify each fraction to its lowest terms.

Part (d): Choosing the correct statements

The three pairs of statements to evaluate are:

1. The angles in $\triangle ABC$ have the same measures as the angles in $\triangle DEF$.
   True, because all corresponding angles match.

2. The angles in $\triangle ABC$ do not have the same measures as the angles in $\triangle DEF$.
   False, as shown in part (a).

3. The ratios of corresponding side lengths are all equal.
   This depends on the results of part (c). If all three ratios are equal, this is True, otherwise False.

4. The ratios of corresponding side lengths are not all equal to each other.
   This is the negation of the third statement.

Would you like detailed help with measuring side lengths or checking ratios? Here are five follow-up questions to consider:

1. Can you confirm the side lengths for $\triangle ABC$ and $\triangle DEF$?
2. Would you like help simplifying the ratios from part (c)?
3. Are $\triangle ABC$ and $\triangle DEF$ similar based on your findings?
4. What geometric properties suggest the triangles are similar (or not)?
5. Would you like a deeper explanation of how ratios relate to triangle similarity?

Tip: Always verify angle measures first when analyzing triangle similarity!