Triangle Congruence: ASA and AAS

Question 1

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

Revolt · Accepted Answer

not enough information given

Question 2

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.

Revolt · Accepted Answer

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.

Question 3

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.

Revolt · Accepted Answer

Selection 1: LNM; Selection 2: MLN; Selection 3: reflexive property; Selection 4: ASA

Question 4

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?

Revolt · Accepted Answer

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

Question 5

Determine the rigid transformations that will map ΔABC to ΔXYZ.

Revolt · Accepted Answer

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

Triangle Congruence: ASA and AAS Answers

More from this Course

TRY EDGENUITY HACKS