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
â–³ SRT, see solution.
B
b
FH, see solution.
C
c
∠K, see solution.
Practice makes perfect
a
Let's focus on triangle â–³ 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 â–³ Y X Z and â–³ 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 JIf 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
