Respuesta :
Answer:
Step-by-step explanation:
Given:
∠2 and ∠4 are the vertical angles
To prove:
∠2 ≅ ∠4
Solution:
Statements Reasons
1). ∠2 and ∠4 are the vertical angles 1). Given
2). Lines m and n intersect at P. 2). Definition of vertical angles
2). ∠2 and ∠3 are the linear pairs 2). Given in the diagram
3). ∠2 + ∠3 = 180° 3). Linear pair theorem
4). ∠3 and ∠4 are the linear pairs 2). Given in the diagram
5). ∠3 + ∠4 = 180° 5). Linear pair theorem
6). ∠2 + ∠3 = ∠3 + ∠4 6). Transitive Property
7). ∠2 ≅ ∠4 7). Subtraction property
Any location at which two lines converge will have the same opposing angle subtended by it. It is proved that ∠2 ≅ ∠4.
What is angle measurement?
An angle measure is the measurement of the angle created by two rays or arms at a shared vertex in geometry. A protractor is used to measure angles in degrees (°).
Given,
∠2+∠3=180°
∠3+∠4=180°
Equating both the equation we get;
∠2=∠4
Statement;
Lines m and n intersect at p.
Reason;
If two lines intersect at any point the opposite angle subtended by the intersecting point will be the same.
Statement;
∠2 + ∠3 = 180°
Reason;
linear pair theorem states that the linear angle has the sum of 180°.
Statement;
∠2 + ∠3 = 180°
Reason;
linear pair theorem states that the linear angle has the sum of 180°.
Statement;
∠3 + ∠4 = 180°
Reason;
linear pair theorem states that the linear angle has the sum of 180°.
Statement;
∠2 + ∠3 = ∠3 + ∠4
Reason;
Transitive Property
Statement;
∠2 ≅ ∠4
Reason;
Subtraction property
Hence, it is proved that ∠2 ≅ ∠4.
To learn more about the angle measurement, refer to the link;
https://brainly.com/question/14684647
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