a Start with looking at the given angle congruences.
B
b Use colors to indicate corresponding vertices in the given triangle congruence.
C
c Use colors to indicate corresponding vertices in the given triangle congruence.
A
a △ SRT, see solution.
B
b FH, see solution.
C
c ∠ K, see solution.
Practice makes perfect
a Let's focus on triangle △ YXZ and the congruences involving the vertices of this triangle. Let's use colors for the vertices mentioned in the given angle congruences.
∠ Y&≅∠ S
∠ X&≅∠ R
∠ T&≅∠ Z
Let's use these colors on the diagram to indicate corresponding vertices.
Notice that this coloring also matches the given segment congruences.
T S&≅ Z Y
X Y&≅ R S
T R&≅ Z X
This means that in triangles △ Y X Z and △ S R T all three corresponding angles and all three corresponding segments are congruent.
By the definition of congruence, this means that these two triangles are congruent.
△ Y X Z≅△ S R T
b Let's focus now on the triangle congruence given in the question. Let's use colors for corresponding vertices indicated by the order of the letters in the congruence.
△ H G F≅△ L K J
If two triangles are congruent, then the corresponding segments are also congruent.
Investigating the colors, we can find that the segment corresponding to J L is F H. Since corresponding segments of congruent triangles are congruent, we found a segment congruent to J L.
J L≅ F H
c This part can also be answered by investigating the given triangle congruence.
△ H G F≅△ L K J
The colors indicate corresponding vertices.
Since corresponding angles of congruent triangles are congruent, the angle congruent to ∠ G has a vertex of the same color. This vertex is K.
∠ G≅∠ K
