Let's analyze the questions shown in the image and discuss the solutions.

Question 4:

Given: ∠HIJ ≅ ∠LJK, HJ ≅ JL. The question is asking which pair of triangles is congruent based on this information.

• Since two angles and the included side are given (Angle ∠HIJ, side HJ, and angle ∠LJK), the triangles can be proven congruent by the SAS (Side-Angle-Side) Postulate.

• The correct answer is ΔHIJ ≅ ΔLJK by SAS, which is marked.

Question 5:

This question asks whether you can use the SAS Postulate or the AAS Theorem to prove the triangles congruent. The hint suggests using the Third Angle Theorem.

• The given triangle appears to have a right angle (90°) and some side lengths marked, which typically leads to the application of the SAS Postulate. However, there might not be enough information to conclude based on either of these two theorems in this case.

• The answer selected is "neither", which seems appropriate if there is not enough information to apply either theorem.

Question 6:

The question asks which pair of triangles is congruent by ASA (Angle-Side-Angle).

• In the correct option selected, the pair of triangles shows two angles and the included side congruent. This fits the ASA Theorem, which states that two triangles are congruent if two angles and the included side are congruent.

• The selected answer is the second pair of triangles, which is correct for ASA.

Would you like more details on any of these questions or further clarifications?

Follow-up questions:

1. How does the SAS Postulate differ from the ASA Theorem in proving congruence?
2. Can the AAS Theorem always be used interchangeably with the ASA Theorem?
3. What is the Third Angle Theorem, and when is it applicable?
4. How does congruence by SSS (Side-Side-Side) differ from SAS or ASA?
5. Could you apply the HL (Hypotenuse-Leg) theorem to any of these questions?

Tip:

Always ensure that the side mentioned in ASA or SAS is the one included between the two angles (for ASA) or one of the angles (for SAS).