Chelsea drew two parallel lines KL and MN intersected by a transversal PQ, as shown below: Two parallel lines KL and MN with PQ
as a transversal intersecting KL at point R and MN at point S. Angle KRP is shown congruent to angle MSP. Which theorem could Chelsea use to show the measure of angle KRP is equal to the measure of angle QRL?
1 answer:
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Answer:
m = 5
Step-by-step explanation:
Since the points are collinear, they all lie on the same line and have the same slope between them.
Calculate the slope m using the slope formula
m =
with (x₁, y₁ ) = (2, 3) and (x₂, y₂ ) = (3, 6)
m = =
= 3
Now calculate the slope using 2 other points and equate to 3
(x₁, y₁ ) = (3, 6) and (x₂, y₂ ) = (m, 12)
m = =
= 3 ( multiply both sides by m - 3 )
6 = 3(m - 3) ← divide both sides by 3
2 = m - 3 ( add 3 to both sides )
5 = m