Can you conclude that triangle GHF is congruent to triangle GJK? Explain.
LNM LON LMN ✔ MLN
substitution property ✔ reflexive propertyaddition property subtraction property
vertical angles ✔ ASAAAA the reflexive property
Are the triangles congruent? If so, how do you know?
✔ LNMLON LMN NLM
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 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
If two triangles have three congruent, corresponding angles, what additional information is needed to prove that the triangles are congruent?
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.
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.
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 interior angle measures of a triangle add up to 180 degrees. Thus, if you are given angle-angle-side, you can solve for the third angle measure and essentially have angle-side-angle because the given side will now be the included side.
What did you include in your response? Check all that apply.
What did you include in your response? Check all that apply.
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