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Pentagon D F G H J is shown inside of pentagon A B C D E.
ABCDE ~ GHJDF. Complete the statements.
∠H≅□
GHDJ=AB□
To complete the statements, we need to find the missing angles and the ratio between corresponding sides.
Since pentagon ABCDE is similar to pentagon GHJDF, we know that the corresponding angles are congruent and the corresponding sides are in proportion.
1. ∠H is congruent to ∠A. This is because corresponding angles in similar polygons are congruent.
2. GHDJ is in proportion to AB. This means that the ratio of their side lengths is equal. We can represent this as:
GHDJ/AB = □/1
Now, let's find the value of □ by comparing the side lengths:
GHDJ has 4 sides, and AB has 5 sides since they are pentagons. So the ratio is:
GHDJ/AB = 4/5
We can substitute this ratio into the proportion equation:
4/5 = □/1
Solving for □, we can cross multiply:
4 = 5□
Divide both sides by 5:
□ = 4/5
Therefore, the completed statements are:
∠H ≅ ∠A
GHDJ = AB(4/5)