Mathematics
Grade9
Easy

Question

Copy and complete the proof.

GIVEN rightwards double arrow R T equals 5 comma R S equals 5 comma stack R T with minus on top approximately equal to stack T S with minus on top
PROVE stack R S with minus on top approximately equal to stack T S with minus on top
What is reason 1 and reason 5?
Statements Reasons
1. Error converting from MathML to accessible text. 1. ____ ?
2. RS = RT 2. Transitive Property of Equality
3. RT = TS
3. Definition of congruent segments
4. RS = TS 4. Transitive Property of Equality
5. Error converting from MathML to accessible text.  5. _____?

  1. Reason 1 - Given, Reason 5 - Definition of midpoint
  2. Reason 1 - Definition of congruency, Reason 5 - Given
  3. Reason 1 - Given, Reason 5 - Definition of congruency
  4. Reason 1 - Definition of midpoint, Reason 5 - Conclusion

Hint:

In this question, We have triangle RST in which, we are given a RT =5, RS = 5, (RT) ̅ ≅ (TS) ̅ and here we have to prove is (RS) ̅ ≅ (TS) ̅  . Here 5 total step were given and also asked the reason of 1st step and 5th step. Use the property of equality.

The correct answer is: Reason 1 - Given, Reason 5 - Definition of congruency


    We have to find the reason of 1st step and 5th step.
    Firstly , we are given a triangle RST , in which given is RT =5, RS = 5, (RT) ̅ ≅ (TS) ̅ .
    Now,
    Statement Reason
    1. RT =5, RS = 5, (RT) ̅ ≅ (TS) ̅ 1. Given
    2. RS = RT 2. Transitive property of Equality
    3. RT = TS 3. Definition of congruent segments
    4. RS = TS 4.Transitive Property of equality
    5. (RS) ̅ ≅ (TS) ̅ 5. Definition of Congruency
    Therefore, the reason of step 1 is given and step 5 is definition of congruency.
    The correct answer is Reason 1 – Given , Reason 5 – Definition of Congruency.


     
     

    In this question , we have to find the reason of step 1 and 5 , here step 1 is already given and step 5 is definition of congruency. Here we already proved that RS = TS so if two lines are equal then they are also congruent.

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