Math Problem Statement
Complete the proof that \( \angle J \cong \angle K \) given that \( \angle K \) and \( \angle I \) are complementary and \( \angle J \) and \( \angle I \) are complementary.
Solution
The image shows a proof table where we need to complete the reasoning to show that . Let's complete the proof.
Given:
- and are complementary.
- and are complementary.
Proof Steps:
Statement | Reason |
---|---|
1. and are complementary | Given |
2. and are complementary | Given |
3. | Definition of complementary angles |
4. | Definition of complementary angles |
5. | Transitive Property of Equality (both sums equal 90°) |
6. | Properties of addition, subtraction (subtract from both sides) |
7. | Definition of congruent angles (equal measures) |
This completes the proof that .
Would you like further details or explanations on any part of this proof? Here are a few related questions that could deepen understanding:
- Why are angles considered complementary when their sum is 90 degrees?
- Can the transitive property of equality be applied in cases other than equality of angles?
- How is the definition of congruent angles connected to their measures?
- Could a similar approach be used to prove angles are supplementary instead of complementary?
- What happens if two angles are neither complementary nor supplementary?
Tip: When proving congruence or equality of angles, always ensure that the definitions of complementary, supplementary, and congruent angles are clearly understood.
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Math Problem Analysis
Mathematical Concepts
Geometry
Angle Relationships
Formulas
m∠K + m∠I = 90°
m∠J + m∠I = 90°
Theorems
Definition of Complementary Angles
Transitive Property of Equality
Definition of Congruent Angles
Suitable Grade Level
Grades 7-10