Triangle Congruence: ASA and AAS Assignment

It is given that angle LNO is congruent to angle _______ and angle OLN is congruent to angle ________. We know that side LN is congruent to side LN because of the _____________. Therefore, because of _______, we can state that triangle LNO is congruent to triangle LNM.

First blank: LNM Second blank: MLN Third blank: reflexive property Fourth blank: ASA

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.

Marcus 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.

Sample Response: 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. Please don't use this as your answer or else it plagiarism. Thanks!

If two triangles have three congruent, corresponding angles, what additional information is needed to prove that the triangles are congruent?

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. Please don't copy, its plagiarism. Use it as an example please!

Determine the rigid transformations that will map ΔABC to ΔXYZ.

Translate vertex X to vertex A; rotate ΔXYZ to align the sides and angles.

Can you conclude that triangle GHF is congruent to triangle GJK? Explain.

not enough information given

Are the triangles congruent? If so, how do you know?

yes, because of ASA or AAS

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 XY ≅ FE

Given: AB || DC∠A ≅ ∠D Prove: ΔABC ≅ ΔDCB 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?

∠ABC ≅ ∠DCB; alternate interior angles of parallel lines are congruent