Math Problem Statement

What is the statement for line 3? Use mangle(angle#) as needed. For example, mangle(1) yields m∠1.

Solution

To determine the correct statement for line 3 in the proof, let us analyze the information provided:

  1. Line 1 states that ∠1 and ∠3 are complementary angles, and ∠1 ≅ ∠2 (meaning ∠1 is congruent to ∠2). This is given.

  2. Line 2 follows the definition of complementary angles, establishing that m1+m3=90m\angle1 + m\angle3 = 90^\circ.

  3. 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:

    m1=m2m\angle1 = m\angle2.

This allows substitution in later steps, as seen in line 4.

Final Statement for Line 3:

m1=m2m\angle1 = m\angle2.

Would you like further clarification on this proof or additional examples? Here are five follow-up questions:

  1. Why is the substitution property of equality used in line 4?
  2. What are complementary angles, and how do they help in this proof?
  3. Could we prove this in reverse order, starting from line 5?
  4. How does congruence relate to the measure of angles in geometric proofs?
  5. 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