Let's use colors to indicate corresponding vertices in the given congruence.
△ A B C≅△ F G H
We will use these colors on the diagram.
Be careful! The way the triangles are drawn suggests a correspondence of vertices, but it is not the correspondence given in the congruence statement.
This diagram is not drawn to scale.
Considering a Congruent Side Pair
Let's focus on one of the congruent side pairs.
A BandF G
Since these are corresponding sides in congruent triangles, their measure is the same.
This allows us to set up and solve an equation for x.
The value that makes segments A B and F G congruent is x=3.
Checking the Other Side Pairs
If triangles â–³ A B C and â–³ F G H are congruent, then the other corresponding sides are also congruent.
Let's check whether this is true when x=3.
First we check the length of sides B C and G H.
These equalities show that for x=3 all three sides of triangle â–³ A B C are congruent to the corresponding side of â–³ F G H.
Hence, by the Side-Side-Side (SSS) Congruence Postulate, these two triangles are congruent for x=3.
Checking Our Answer
Scaled diagram
Since the diagram in the book is not drawn to scale, you might wonder what the actual triangles look like.
