Math Problem Statement
Solution
To determine the correct statement for line 3 in the proof, let us analyze the information provided:
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Line 1 states that ∠1 and ∠3 are complementary angles, and ∠1 ≅ ∠2 (meaning ∠1 is congruent to ∠2). This is given.
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Line 2 follows the definition of complementary angles, establishing that .
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Line 3 must then utilize the fact that ∠1 is congruent to ∠2. By the Definition of Congruent Angles, congruent angles have equal measures. Hence, we can state in line 3:
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This allows substitution in later steps, as seen in line 4.
Final Statement for Line 3:
.
Would you like further clarification on this proof or additional examples? Here are five follow-up questions:
- Why is the substitution property of equality used in line 4?
- What are complementary angles, and how do they help in this proof?
- Could we prove this in reverse order, starting from line 5?
- How does congruence relate to the measure of angles in geometric proofs?
- Can the reasoning in this proof be applied to other geometric properties, like supplementary angles?
Tip: When working on proofs, ensure each statement logically follows from the previous one and aligns with the reason provided.
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Math Problem Analysis
Mathematical Concepts
Geometry
Complementary Angles
Congruence
Formulas
m∠1 + m∠3 = 90° (definition of complementary angles)
Theorems
Definition of Congruent Angles
Suitable Grade Level
Grades 9-10