Question

Drag a statement or reason to each box to complete this proof.

Given: the measure of angle A C D equals 60 degrees. Prove: triangle A B C is an obtuse triangle. Art: A triangle A B C. Side B C of the triangle is extended as a ray through point D.
Statements Reasons
1. m∠ACD=60° Given

2. ∠ACD and ∠ACB are supplementary. _____________________________

3. m∠ACD+m∠ACB=180° Definition of supplementary angles

4. _________________________ Substitution Property of Equality

5. _________________________ Subtraction Property of Equality

6. ∠ACB is an obtuse angle. ___________________________

7. △ABC is an obtuse triangle. Definition of obtuse triangle

A. m∠ACB=120°
B. 60°+m∠ACB=180°
C. Definition of obtuse angle
D. Linear Pair Postulate

Answer 1

1. m∠ACD=60° Given

2. ∠ACD and ∠ACB are supplementary Linear Pair Postulate

3. m∠ACD+m∠ACB=180° Definition of supplementary angles

4. 60°+m∠ACB=180° (Substitute 60° on the place of m∠ACD) Substitution property of equality

[The substitution property of equality says that if a=b, then 'a' can be substituted in for 'b' in any equation or vice versa]

5. m∠ACB=120° [Subtract 60° from the both sides] Subtraction Property of Equality

[Subtraction property of equality says that if we subtract from one side of an equation,then it must be subtracted from the other side of the equation to keep the equation the same.]

6. ∠ACB is an obtuse angle. Definition of obtuse angle

[An obtuse angle is an angle of greater than 90° and less than 180°.]

7. △ABC is an obtuse triangle. Definition of obtuse triangle

Answer 2

Statement Reason

1. m∠ACD=60° ------------- Given

2. ∠ACD and ∠ACB are supplementary---------- Linear Pair Postulate

3. m∠ACD+m∠ACB=180° --------- Definition of supplementary angles

4. 60°+m∠ACB=180° ------------------------- Substitution property

5.m∠ACB=120° ----------------Simplifying (Subtraction Property of Equality)

6. ∠ACB is an obtuse angle. ----------------Definition of Obtuse angle

7. △ABC is an obtuse triangle. -------------Definition of obtuse triangle

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