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 â–³ ABC is congruent to two sides of triangle â–³ DEF.
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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 â–³ DEF is greater than the included angle measure in triangle â–³ ABC.
m ∠D>m ∠A
