Answer:
Dangling constructions are parts of sentences that are located in the wrong position and therefore mislead the reader that they refer to something else other than what the author intended.
Q1. Dates became a burden to me, as I was naturally shy.
The way the original sentence was written, it would seem that 'dates' are naturally shy, and not 'me.'
Q2. Our ranch can easily be seen if you look north.
The way the original sentence was written, it would seem that the 'ranch' was performing the action of looking north.
Q3. While I was climbing to the roof, the ladder slipped and made me fall.
If you add the pronoun I, you will make sure that you were the one climbing to the roof and not the ladder.
Q4. By being ignored. Johnny stopped having tantrums.
If you make Johnny the object of being ignored, you will avoid a dangling construction.
Q5. Dad set a trap by the chrysanthemums because they were eaten by gophers.
The way the original sentence was written, it would seem that 'Dad' was eaten by gophers, and not the flowers.
Q6. When Don was nine, his father died of a cerebral hemorrhage.
The way the original sentence was written, it would seem that Don's dad was nine years old when he died.
Q7. To sew properly, you should follow a pattern.
It's important to write who will be performing the action.
Q8. To achieve success in any field, you must maintain perseverance.
The same as the previous sentence.
Q9. By arriving at the fair early, you can see the winning entries.
The same as the previous sentence.