Problem 2 Using Properties of Equality and Congruence

What is the name of the property of equality or congruence that justifies going from the first statement to the second statement?

1. 2 x + 9 = 19 2 x = 10 Subtraction Property of Equality  table with 2 rows and 2 columns , row1 column 1 , 2 x plus , 9 , column 2 equals 19 , row2 column 1 , 2 x , column 2 equals 10 , column 3 cap subtractioncap propertyofcap equality , end table
2. ∠ O ≅ ∠ W  and  ∠ W ≅ ∠ L ∠ O ≅ ∠ L Transitive Property of Congruence  table with 2 rows and 2 columns , row1 column 1 , angle o , column 2 approximately equal to , angle w , and , angle w , approximately equal to , angle l , row2 column 1 , angle o , column 2 approximately equal to , angle l , column 3 cap transitivecap propertyofcap congruence , end table
3. m ∠ E = m ∠ T m ∠ T = m ∠ E Symmetric Property of Equality  table with 2 rows and 1 column , row1 column 1 , m angle , e equals , m angle t , row2 column 1 , m angle , t equals , m angle e , column 2 cap symmetriccap propertyofcap equality , end table

✓ Got It?

2. For parts (a)−(c), what is the name of the property of equality or congruence that justifies going from the first statement to the second statement?

   1. A R ¯ ≅ T Y ¯ T Y ¯ ≅ A R ¯ table with 2 rows and 1 column , row1 column 1 , eh r bar , approximately equal to , t y bar , row2 column 1 , t y bar , approximately equal to , eh r bar , end table
   2. 3 ( x + 5 ) = 9 3 x + 15 = 9 table with 2 rows and 1 column , row1 column 1 , 3 open x plus , 5 close equals 9 , row2 column 1 , 3 x plus . 15 equals , 9 , end table
   3. 1 4 x = 7 x = 28 table with 2 rows and 2 columns , row1 column 1 , 1 fourth , x equals , column 2 7 , row2 column 1 , x equals , column 2 28 , end table
   4. Reasoning What property justifies the statement m ∠ R = m ∠ R ? m angle , r equals , m angle r question mark