What additional information could be used to prove that ΔXYZ ≅ ΔFEG using ASA or AAS? Check all that apply.∠Z ≅ ∠G and XZ ≅ FG∠Z ≅ ∠G and ∠Y ≅ ∠EXZ ≅ FG and ZY ≅ GEXY ≅ EF and ZY ≅ FG∠Z ≅ ∠G and XY ≅ FE
Sample Response: To prove that two triangles with three congruent, corresponding angles are congruent, you would need to have at least one set of corresponding sides that are also congruent. You could then use ASA or AAS congruence theorems or rigid transformations to prove congruence. What did you include in your response? Check all that apply.Congruent, corresponding side lengths are needed.The triangles need corresponding, congruent sides to be congruent.Once congruent sides are known, the AS
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Can you conclude that triangle GHF is congruent to triangle GJK? Explain.
If two triangles have three congruent, corresponding angles, what additional information is needed to prove that the triangles are congruent?
To prove that the triangles are congruent, you would need to know that at least one pair of corresponding side lengths is also congruent. Having congruent corresponding angles only proves that the triangles are similar. Once a pair of congruent corresponding sides is identified, the triangles can be proven congruent using the ASA (Angle-Side-Angle) or AAS (Angle-Angle-Side) congruence theorems.
During geometry class, students are told that ΔTSR ≅ ΔUSV. Marcus states that ΔTSR is mapped to ΔUSV by performing a rotation about point S. Sam states that ΔTSR is mapped to ΔUSV by a reflection across the line that goes through point S. Determine if either student is correct.
Are the triangles congruent? If so, how do you know?
Explain how the angle-angle-side congruence theorem is an extension of the angle-side-angle congruence theorem. Be sure to discuss the information you would need for each theorem.
The AAS congruence theorem is considered an extension of the ASA theorem because of the Triangle Angle Sum Theorem, which states that the interior angles of a triangle sum to 180 degrees. If you are given two angles and a non-included side (AAS), you can subtract the sum of the two known angles from 180 to find the third angle. Once you have the third angle, the given side becomes the included side between two known angles, effectively converting the AAS information into ASA information.
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Isabelle proves that the triangles are congruent by using the parallel lines to determine a second set of angles are congruent. What statement and reason could she have used?
Determine the rigid transformations that will map ΔABC to ΔXYZ.
What did you include in your response? Check all that apply.
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