Given triangle ABC is congruent to triangle PQR, triangle PQR is congruent tp triangle XYZ, prove that triangle ABC is congruent to triangle XYZ
think transitive property, working on each side
To prove that triangle ABC is congruent to triangle XYZ, we need to use the transitive property of congruence.
1. Given triangle ABC ≅ triangle PQR and triangle PQR ≅ triangle XYZ
2. We know that if two triangles are congruent, their corresponding sides and angles are congruent.
So, we have:
AB ≅ PQ (By the definition of congruent triangles)
BC ≅ QR
AC ≅ PR
∠A ≅ ∠P
∠B ≅ ∠Q
∠C ≅ ∠R
3. Now, we need to show that triangle ABC is congruent to triangle XYZ.
We can do this by showing that their corresponding sides and angles are congruent.
By using the transitive property of congruence, we can say that:
AB ≅ PQ ≅ XY (By transitive property)
BC ≅ QR ≅ YZ
AC ≅ PR ≅ XZ
∠A ≅ ∠P ≅ ∠X
∠B ≅ ∠Q ≅ ∠Y
∠C ≅ ∠R ≅ ∠Z
4. Therefore, all corresponding sides and angles of triangle ABC and triangle XYZ are congruent.
Hence, by the definition of congruent triangles, triangle ABC is congruent to triangle XYZ.