Statement Reason 1. m angle cap h is equal to 30 degrees , m angle cap j is equal to 50 degrees , m angle cap p is equal to 50 degrees , m angle cap n is equal to 100 degrees 1. given 2. m angle cap h plus m angle cap j plus m angle cap k is equal to 180 degrees 2. ? 3. 30 degrees plus 50 degrees plus m angle cap k is equal to 180 degrees 3. substitution property 4. 80 degrees plus m angle cap A is equal to 180 degrees 4. addition 5. m angle cap k is equal to 100 degrees 5. subtraction property of equality 6. m angle cap j is equal to m angle cap p ; m angle cap k is equal to m angle cap n 6. substitution 7. angle cap j is congruent to angle cap p ; angle cap k is congruent to angle cap n 7. if angles are equal then they are congruent 8. triangle HKJ approximates triangle LNP 8. AA similarity theorem Which reason is missing in step 2?
Answer
A
definition of supplementary angles
B
triangle angle sum theorem
C
CPCTC
D
triangle parts relationship theorem
Explanation
Angles H, J, and K are the three interior angles of triangle HKJ. The measures of a triangle’s interior angles add to 180 degrees, so step 2 follows from the triangle angle sum theorem. This is choice B.
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