Math Problem Statement

Identify the triangle congruence and rigid motion based on the given diagram.

Solution

From the image, we are tasked with identifying the triangle congruence and the type of rigid motion for the two triangles shown.

Key Observations:

  1. Congruence Markings:

    • The triangles share side FG, and this side is marked the same in both triangles.
    • ∠HFG in the top triangle corresponds to ∠LFH in the bottom triangle, indicated by identical angle markings.
    • Side FH in the top triangle corresponds to side FL in the bottom triangle, as marked.

    This matches the SAS (Side-Angle-Side) congruence criterion.

  2. Rigid Motion:

    • The shape of the triangles and their orientation indicate a Reflection across line FG.

Correct Answer:

The correct choice is SAS, Reflection.


Would you like me to explain any part of this solution further or discuss related concepts?

Here are 5 related questions you might find helpful:

  1. How do you identify the correct congruence criteria for triangles?
  2. What are rigid motions, and how are they applied to geometric figures?
  3. Can you explain the difference between reflection and rotation?
  4. Why is SAS a valid method to prove triangle congruence?
  5. How can we determine the axis of reflection in such problems?

Tip: When solving triangle congruence problems, always carefully check for corresponding sides and angles to match a specific congruence criterion.

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Math Problem Analysis

Mathematical Concepts

Triangle Congruence
Rigid Motions
Reflection
SAS Congruence

Formulas

SAS Congruence Criterion

Theorems

Side-Angle-Side (SAS) Triangle Congruence Theorem

Suitable Grade Level

Grades 7-10