Question

try this video for extra example 3 - writing a two-column proof

1. use the reason bank below to write a two - column proof for the given situation.

given: ∠1 is supplementary to ∠3
∠2 is supplementary to ∠3
prove: ∠1 ≅ ∠2

statements	reasons
2. m∠1 + m∠3 = 180°	2.
3. ∠2 is supplementary to ∠3.	3.
4. m∠2 + m∠3 = 180°	4.
5. m∠1 + m∠3 = m∠2 + m∠3	5.
6. m∠1 = m∠2	6.
7. ∠1 ≅ ∠2	7.

reasons bank
subtraction property of equality definition of supplementary angles (×2)
division property of equality given
definition of congruent angles substitution property of equality

explain 2 using properties of congruence
visit bim.easyaccessmaterials.com, read integrated mathematics 1 lesson 9.4, then read the section below.
teacher voice - a theorem is a statement that can be proven. below are some theorems that state that segment and angle congruence is reflexive, symmetric, and transitive. each of the following theorems can be proven.
once a theorem is proven, it can be used in subsequent proofs. the proven theorem is then a tool or strategy that helps in proving a new statement.
you will prove some of these theorems in the homework and exercises that follow.

properties of segment congruence
reflexive for any segment ab, (overline{ab} cong overline{ab}).
symmetric if (overline{ab} cong overline{cd}), then (overline{cd} cong overline{ab}).
transitive if (overline{ab} cong overline{cd}), and (overline{cd} cong overline{ef}), then (overline{ab} cong overline{ef}).

properties of angle congruence
reflexive for any angle a, ∠a ≅ ∠a
symmetric if ∠a ≅ ∠b then ∠b ≅ ∠a
transitive if ∠a ≅ ∠b and ∠b ≅ ∠c then ∠a ≅ ∠c

Explanation:

Step1: Match given statement

Reason: Given

Step2: Def. of supplementary angles

Reason: Definition of supplementary angles

Step3: Match given statement

Reason: Given

Step4: Def. of supplementary angles

Reason: Definition of supplementary angles

Step5: Substitute equal expressions

Reason: Substitution Property of Equality

Step6: Subtract $m\angle3$ from both sides

Reason: Subtraction Property of Equality

Step7: Def. of congruent angles

Reason: Definition of congruent angles

Answer:

STATEMENTS	REASONS
2. $m\angle1 + m\angle3 = 180^\circ$	2. Definition of supplementary angles
3. $\angle2$ is supplementary to $\angle3$.	3. Given
4. $m\angle2 + m\angle3 = 180^\circ$	4. Definition of supplementary angles
5. $m\angle1 + m\angle3 = m\angle2 + m\angle3$	5. Substitution Property of Equality
6. $m\angle1 = m\angle2$	6. Subtraction Property of Equality
7. $\angle1 \cong \angle2$	7. Definition of congruent angles