When two angles have the same number of markers, this indicates that the angles are congruent. Similarly, when two sides have the same number of markers, the sides are congruent.
Corresponding Angles: ∠ X ≅ ∠ J, ∠ Y ≅ ∠ K, ∠ Z ≅ ∠ L Corresponding Segments: XY ≅ JK, YZ ≅ KL, ZX ≅ LJ Congruence Relation: △ XYZ≅△ JKL
The angle measures tell us about the congruence relationships between the angles of the triangles.
∠ X &≅ ∠ J
∠ Y &≅ ∠ K
∠ Z &≅ ∠ L
All angles in △ XYZ have congruent pairs in △ JKL.
Checking Sides
Now let's check the sides.
The markers on the sides and the given side length tell us about the congruence relationships between the sides of the triangles.
XY &≅ JK
YZ &≅ KL
ZX &≅ LJ
All sides of △ XYZ have congruent pairs in △ JKL.
Conclusion
Since the vertices of the two triangles can be paired up so that the corresponding angles and sides are congruent, the two triangles are congruent.
△ XYZ ≅△ JKL
