1.)Explain why ironing boards always remain parallel to the floor and can be adjusted for people of various heights. You may want to consider the following:
a.)The legs of the board are built so that AD = BD and DE = DF, and ADF and BDE are straight lines as shown.
b.)Which angles are equal? Why?
c.)Join EF. Which triangles are similar? Why? Name three other objects that demonstrate this property and explain why they are designed in that way.
To explain why ironing boards always remain parallel to the floor and can be adjusted for people of various heights, let's consider the given information:
a.) The legs of the board are built so that AD = BD and DE = DF, and ADF and BDE are straight lines.
b.) The angles that are equal in this scenario are angles ADF and BDE. This is because AD = BD and DE = DF, which indicates the legs are symmetrical. When the legs are symmetrical, the angles opposite to equal sides are also equal. Therefore, angles ADF and BDE are equal.
c.) Joining EF reveals the similarity of triangles ADF and BDE. These two triangles are similar because they have proportional sides and equal corresponding angles.
Three other objects that demonstrate this property of similar triangles are:
1. Step ladders: Step ladders typically have parallel sides at each step, allowing the ladder to maintain balance and adjust according to the desired height. The sides of each step (similar to the legs of the ironing board) are built proportionally, forming similar triangles.
2. Telescopic antennas: Telescopic antennas are designed with nested tubes that can be extended to different lengths. These tubes are proportional in size, allowing the antenna to maintain its parallel alignment with the ground. The nested tubes form similar triangles similar to the legs of the ironing board.
3. Camera tripods: Camera tripods have adjustable legs that can be extended or contracted based on the desired height. The legs of the tripod are designed with proportional sections, allowing the tripod to remain parallel to the ground and adjust according to the user's needs. Similar triangles are formed in the legs of the tripod, just like in the legs of the ironing board.
In summary, the similarity of triangles in the legs of the ironing board ensures that it remains parallel to the floor and can be adjusted for people of various heights. This principle is also applied in various other objects such as step ladders, telescopic antennas, and camera tripods to maintain stability and flexibility.