Mathematics: Given: ∠1 , ∠2 , ∠3 , and ∠4 formed by two intersecting segments. prove: ∠2 and ∠4 are congruent. (look at image down below)

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Given: ∠1 , ∠2 , ∠3 , and ∠4 formed by two intersecting

Ответ:

LunaSpellman

10.03.2022

Mathematics

Answer :

1. $\angle 2+\angle 3=180^{\circ}$

2.Linear postulate

3. $\angle 2+\angle 3=\angle 3+\angle 4$

4.Subtraction property of equality

Step-by-step explanation:

We are given that angle 1. angle 2, angle 3 and angle 4 formed by two intersecting segment.

We have to prove that angle 2 and angle 4 are congruent.

Proof:

Statement 1: $\angle 1,\angle 2,\angle 3$ and $\angle 4$ formed by two intersecting lines.

Reason: Given

Statement 2: $\angle 3$ and $\angle 4$ forms linear pair

Reason:By definition of linear pair

Statement 3: $\angle 2$ and forms linear pair

Reason: By definition of linear pair

Statement 4: $\angle 2+\angl 3=180^{\circ}$

Reason: Linear pair postulate

Statement 5: $\angel 3+\angle 4=180^{\circ}$

Reason: Linear pair postulate

Statement 6: $\angle 2+\angle 3=\angle 3+\angle 4$

Reason: By substitution property of equlaity

Statement 7: $\angle 2=\angle 4$

Reason: Subtraction property of equality

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Given: ∠1 , ∠2 , ∠3 , and ∠4 formed by two intersecting segments. prove: ∠2 and ∠4 are congruent. (look at image down below)

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