Corresponding angles:
∠RPQ ≅ ∠PQX, ∠RQP ≅ ∠QPX, and ∠R ≅ ∠X
Corresponding sides:
line QP ≅ line PQ, line RQ ≅ line PX, and line RP ≅ line QX
Step-by-step explanation:
This problem says ΔQPR is congruent to ΔPQX. We can use this phrase to find the congruent sides and angles, and then use the picture to check our answers. The reason for this is that when writing congruent triangles, each letter has to match in the exact order that it is congruent. For example, if we had ΔABC congruent to ΔDEF, angle A would have to be congruent to angle D since they both match up in the order listed. In that same triangle case, line AB would also have to be congruent to line DE, since that is how the line order is listed.
We can use this in this problem. ΔQPR is congruent to ΔPQX, so angle Q would have to be congruent to angle P. Now we can use the picture to check if our claim makes sense.
In the picture, we see that there are multiple angle Qs and angle Ps. There is ∠RQP, ∠PQX, and ∠RQX for ∠Q; and there is ∠RPQ, ∠QPX, and ∠RPX for ∠P. So we have to be specific about which angles we are referring to. We can use ΔQPR and ΔPQX to find out which specific ones. We see that one of the angles is ∠RQP due to the order of ΔQPR being Q → P → R and then repeat. This means we could rearrange it to R → Q → P as long as we also change the order of ΔPQX to X → P → Q. That's how we could get ∠RQP ≅ ∠QPX (if it sounds confusing, look at how the name of the triangles are arranged and why it matters, and look at ∠RQP and ∠QPX in the triangle).
You can repeat this observation process to find the 3 pairs of angles, which will give you ∠RPQ ≅ ∠PQX, ∠RQP ≅ ∠QPX, and ∠R ≅ ∠X (you can type ∠R ≅ ∠X because there is only one ∠R and ∠X).
You follow a similar process with lines. If we had ΔABC congruent to ΔDEF, line AB would be congruent to DE. You see the pattern here? With ΔQPR congruent to ΔPQX, line QP would be congruent to PQ (if you noticed, these lines are the exact same, and that's because of the reflexive property - to know more, visit cuemath.com/algebra/reflexive-property/). This allows you to find line QP ≅ line PQ, line RQ ≅ line PX, and line RP ≅ line QX.
Now the only thing left is to mark them on your triangle. You can use tick marks (the lines) to show 2 lines congruent, but make sure each pair can be distinguished. For example, you can use 1 tick mark for line QP and line PQ, but use 2 for line PX and RQ to show they are a different pair of congruent lines. For angles, you apply the same concept, but instead, you use a loop-like shape. And that will leave you with the result in the picture.