Triangle Congruence: ASA and AAS

Question 1

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

Revolt · Accepted Answer

∠Z ≅ ∠G and XZ ≅ FG; ∠Z ≅ ∠G and XY ≅ FE

Question 2

substitution property ✔ reflexive propertyaddition property subtraction property

Revolt · Accepted Answer

✔ reflexive property

Question 3

vertical angles ✔ ASAAAA the reflexive property

Revolt · Accepted Answer

✔ ASA

Question 4

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

Revolt · Accepted Answer

not enough information given

Question 5

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

Revolt · Accepted Answer

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.

Question 6

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 7

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

Revolt · Accepted Answer

yes, because of ASA or AAS

Question 8

Question 9

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 9

✔ 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 10

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

Triangle Congruence: ASA and AAS Answers

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