a Consider the height of the swing and the length of the rope.
B
b Consider the position of the swing.
A
a AB≅DE AC≅DF
B
b m∠ D>m∠ A, see solution.
Practice makes perfect
a Let's sketch the triangles appearing in the picture.
We are asked to find congruent segments.
Congruent Segments
Justification
AB≅DE
The length of both of these segments is the height of the swing.
AC≅DF
The length of both of these segments is the length of the rope of the swing.
b Our result in Part A shows that two sides of triangle △ ABC is congruent to two sides of triangle △ DEF.
Segment EF is longer than segment BC, because the child on the first picture is closer to the starting position than in the second picture.
EF> BC
According to the Converse of the Hinge Theorem, this means that the included angle measure in triangle △ DEF is greater than the included angle measure in triangle △ ABC.
m ∠ D>m ∠ A
