Mathematical proofs are important because they help to explain concepts. They also serve as concrete validation for a mathematical result or statement.
- In geometry, an incorrect conclusion within a proof might lead to wrong estimations of size, length, and other spatial properties.
- Algebra, topology, arithmetics, calculus, and statistics are some other branches of mathematics. In statistics, an incorrect conclusion within a proof might lead to the wrong interpretation of bulky data. Statistical properties like the mean, median, and mode can be misinterpreted.
- Businesses that rely on statistics for production and forecasting might be affected.
<h3>What is a Mathematical proof?</h3>
A proof in mathematics is a number of conclusions that lead to the justification of a final statement.
Having incorrect mathematical proofs can be dangerous because it will cause the misinterpretation of concepts and the obtaining of wrong results.
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Answer:
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Step-by-step explanation:
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The parts that are missing in the proof are:
It is given
∠2 ≅ ∠3
converse alternate exterior angles theorem
<h3>What is the Converse of Alternate Exterior Angles Theorem?</h3>
The theorem states that, if two exterior alternate angles are congruent, then the lines cut by the transversal are parallel.
∠1 ≅ ∠3 and l║m because we are: given
By the transitive property,
∠2 and ∠3 are alternate interior angles, therefore, they are congruent to each other by the alternate interior angles theorem.
Based on the converse alternate exterior angles theorem, lines p and q are proven to be parallel.
Therefore, the missing parts pf the paragraph proof are:
- It is given
- ∠2 ≅ ∠3
- converse alternate exterior angles theorem
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