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Caroline is given this diagram and told that EG¯¯¯¯¯¯¯¯ is an angle bisector of ∠HEF . She looks carefully and finds one pair of congruent angles between two pairs of congruent sides. She determines that the triangles must be congruent by the SAS Congruent Theorem. Match each pair of congruent corresponding parts with the reason Caroline knows that they are congruent (1 point) Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. EG¯¯¯¯¯¯¯¯ ≅ EG¯¯¯¯¯¯¯¯ ∠EG ≅ ∠EG HE¯¯¯¯¯¯¯¯ ≅ FE¯¯¯¯¯¯¯¯ Skip to navigation

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To match each pair of congruent corresponding parts with the reason Caroline knows that they are congruent by the SAS (Side-Angle-Side) Congruence Theorem, we can break it down as follows:

  1. EG ≅ EG: This represents the shared side in both triangles, which is congruent by definition (reflexive property).

  2. ∠EG ≅ ∠EG: This represents the congruent angles because EG is the angle bisector, which means it divides the angle ∠HEF into two equal angles.

  3. HE ≅ FE: These sides are congruent based on the information provided that the triangles are congruent by the SAS theorem as well.

So, the pairs and their corresponding reasons would be:

  • EG ≅ EG: Reflexive property (shared side).
  • ∠EG ≅ ∠EG: Congruent angles (angle bisector).
  • HE ≅ FE: Corresponding sides are congruent based on the equality established by the triangle congruence.

If you were to place these into specific inputs, assign them as follows:

  1. EG ≅ EG (shared side)
  2. ∠EG ≅ ∠EG (by the angle bisector)
  3. HE ≅ FE (sides of triangles)

This organization aligns logically with the SAS Congruent Theorem geometry principles Caroline is utilizing.