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Math  /  Geometry

Question(4) Explain what is wrong with each of the following. (a) Point QRSQ R S. (b) ACundefined\overleftrightarrow{A C} and BDundefined\overleftrightarrow{B D} bisect each other. (C) Point M≅M \cong Point WW

Studdy Solution

STEP 1

1. Each part of the problem involves understanding basic geometric concepts and definitions.
2. We need to identify the correct terminology and properties of geometric figures and relationships.

STEP 2

1. Analyze and explain the issue with the statement "Point QRSQ R S".
2. Analyze and explain the issue with the statement "ACundefined\overleftrightarrow{A C} and BDundefined\overleftrightarrow{B D} bisect each other".
3. Analyze and explain the issue with the statement "Point M≅M \cong Point WW".

STEP 3

Analyze the statement "Point QRSQ R S".
A point is a single location in space, typically denoted by a single capital letter. The statement "Point QRSQ R S" implies a single point represented by three letters, which is incorrect. Each point should be represented by a single letter.

STEP 4

Analyze the statement "ACundefined\overleftrightarrow{A C} and BDundefined\overleftrightarrow{B D} bisect each other".
To bisect means to divide into two equal parts. Two lines or line segments can intersect, but for them to bisect each other, they must intersect at their midpoints. The statement "ACundefined\overleftrightarrow{A C} and BDundefined\overleftrightarrow{B D} bisect each other" means that the intersection point would be the midpoint of both segments, which is not generally true for all intersecting lines. This statement should specify that the lines are segments and that they intersect at their midpoints.

STEP 5

Analyze the statement "Point M≅M \cong Point WW".
The symbol ≅\cong means "congruent to," which is used for figures that have the same shape and size, such as angles, segments, or geometric shapes. Points are not shapes; they do not have dimensions to compare for congruence. Therefore, stating "Point M≅M \cong Point WW" is incorrect. Instead, it should state that points MM and WW are the same point if they coincide.
Solution: (a) The issue with "Point QRSQ R S" is that a point must be represented by a single letter, not multiple letters. (b) The issue with "ACundefined\overleftrightarrow{A C} and BDundefined\overleftrightarrow{B D} bisect each other" is that for them to bisect each other, they must intersect at their midpoints, which is not generally true for all intersecting lines. (c) The issue with "Point M≅M \cong Point WW" is that the symbol ≅\cong is used for comparing shapes and sizes, not individual points.

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