Mathematics
Grade9
Easy

Question

Write a complete proof by matching each statement with its corresponding reason.
GIVEN: stack Q S with rightwards arrow on top is an angle bisector of angle P Q R.
PROVE: m angle P Q S equals fraction numerator 1 over denominator 2 end fraction m angle P Q R
Statements Reason
stack Q S with rightwards arrow on top is an angle bisector of straight angle P Q R A. Definition of angle bisector
straight angle P Q S approximately equal to straight angle S Q R B. Distributive Property
m straight angle P Q S equals m straight angle S Q R C. Angle Addition Postulate
m straight angle P Q S plus m straight angle S Q R equals m straight angle P Q R D. Given
m straight angle P Q S plus m straight angle P Q S equals m straight angle P Q R E. Division Property of Equality
2 times m straight angle P Q S equals m straight angle P Q R F. Definition of congruent angles
m straight angle P Q S equals 1 half m straight angle P Q R G. Substitution Property of Equality

  1. 1 - A, 2 - B, 3 - C, 4 - D, 5 - E, 6 - F, 7 - G
  2. 1 - G, 2 - F, 3 - A, 4 - B, 5 - C, 6 - E, 7 - D
  3. 1 - D, 2 - F, 3 - A, 4 - C, 5 - G, 6 - B, 7 - E
  4. 1 - D, 2 - F, 3 - A, 4 - E, 5 - B, 6 - G, 7 - C

Hint:

In this question , we have to match the statement to the correct reasons. Given is (QS ) ⃗ is an angle bisector of ∠PQR. Remember the property of equality to match them.

The correct answer is: 1 - D, 2 - F, 3 - A, 4 - C, 5 - G, 6 - B, 7 - E


    Here we have to match the statement to the correct reasons.
    We have given (QS ) ⃗ is an angle bisector of ∠PQR.
    Now,
    Statements Reason
    Statements Reason
    stack Q S with rightwards arrow on top is an angle bisector of straight angle P Q R A. Definition of angle bisector
    straight angle P Q S approximately equal to straight angle S Q R B. Distributive Property
    m straight angle P Q S equals m straight angle S Q R C. Angle Addition Postulate
    m straight angle P Q S plus m straight angle S Q R equals m straight angle P Q R D. Given
    m straight angle P Q S plus m straight angle P Q S equals m straight angle P Q R E. Division Property of Equality
    2 times m straight angle P Q S equals m straight angle P Q R F. Definition of congruent angles
    m straight angle P Q S equals 1 half m straight angle P Q R G. Substitution Property of Equality

    The match are:
    1 → D
    2 → F
    3 → A
    4 → C
    5 → G
    6 → B
    3 → E
    Therefore the correct answer is 1-D, 2- F, 3 - A, 4- C, 5 - G, 6 - B, 7-E.

    In this question , we have to match the statements to the correct reasons and for that , Use the Property of Equality and match with correct reason.

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