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The line l and and m are intersect so to proof that the angles are supplementary to one another by using linear pair theorem.
Theorem of linear pairs:
The linear pair postulate or linear pair theorem in mathematics says the same thing. If two angles form a linear pair, their measures add up to 180.
Two angles are supplementary when their measures equals to 180 degrees.
∠2 is supplement to ∠3
∠2 + ∠3 = 180°
∠3 is supplement to ∠4
∠3 + ∠4 = 180°
∠1 is supplement to ∠4
∠1+ ∠4 = 180°
∠2 is supplement to ∠3
∠2 + ∠3 = 180°
∠1 is supplement to ∠2
∠1 + ∠2 = 180°
Hence , through linear pair theorem : ∠1 is supplement to ∠2 and ∠2 is supplement to ∠3
The two angles are congruent if they are supplements of the same angle—also known as congruent angles.
Because angles 1 and 3 are supplements of the same angle 2, we can draw the following conclusion from the preceding statement:
∠1 ≅ ∠3 (congruent supplements theorem)
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Final answer:
The question discusses intersecting lines in geometry. Two lines intersect when they cross at a single point, creating four angles. A flowchart on this can identify the lines, show the intersection, define the intersection point and the resulting angles.
Explanation:
This question relates to the fields of geometry, specifically the concepts of intersecting lines. If lines l and m intersect, it means they cross at a single point. This point of intersection splits each line into two parts and creates four angles.
When creating a flowchart, the first step could be to identify line l and line m. Then, you would show the intersection of these two lines. Next, you define the intersection point and analyze the angles formed by the intersection. The flowchart would end with a statement affirming that lines l and m intersect, creating four angles.
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