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

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.

Revolt · Accepted Answer

Marcus is correct.

Question 3

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

Revolt · Accepted Answer

yes, because of ASA or AAS

Question 4

Question 4

Revolt · Accepted Answer

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: LNM; 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: MLN; 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: reflexive property; 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: ASA

Question 5

✔ LNMLON LMN NLM

Revolt · Accepted Answer

✔ LNM; 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: LNM; 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: MLN; 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: reflexive property; 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: ASA

Question 6

LNM LON LMN ✔ MLN

Revolt · Accepted Answer

✔ MLN

Question 7

substitution property ✔ reflexive propertyaddition property subtraction property

Revolt · Accepted Answer

✔ reflexive property

Question 8

vertical angles ✔ ASAAAA the reflexive property

Revolt · Accepted Answer

✔ ASA

Question 9

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 10

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

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