30. PLis the angle bisector of KPM.Which can you conclude from this statement? You also can see this question number 30 on this website.Please add hyperlink.
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How answer is A and i want to learn how to find a length of KL. Please help.
Because PL bisects ∡KPM,
∡LPJ ≅ ∡LPN
Since both are right triangles, and they share hypotenuse LL, ∆ LPJ ≅ ∆ LPN by ASA. So, LJ ≅ LN
Using similar reasoning, using SAS, ∆LJK ≅ ∆LNM.
So, LN ≅ LJ
oops. typo. they share hypotenuse PL
To find the length of KL, we need to use the angle bisector theorem.
The angle bisector theorem states that in a triangle, if a line divides one of the angles into two equal angles, then it divides the opposite side into two segments that are proportional to the other two sides of the triangle.
In this case, PL is the angle bisector of angle KPM. Let's label the length of KP as x and the length of PM as y.
According to the angle bisector theorem, we know that:
KL / LM = KP / PM
Since PL bisects angle KPM, we can assume that the line is bisecting KP as well. Therefore, we can say that KP = PL.
Using this information, we can rewrite the equation as:
KL / LM = PL / PM
Since we want to find the length of KL, we can rearrange the equation as:
KL = (PL * LM) / PM
Now, to find the length of KL, we need to know the lengths of PL, LM, and PM. Unfortunately, without the given diagram or any other information, we cannot determine the specific lengths of these segments and therefore cannot find the exact length of KL.
As for the given statement, "PL is the angle bisector of KPM," it tells us that PL divides angle KPM into two equal angles. This is just a statement of fact without providing any information about the lengths of the segments. Therefore, we cannot use this statement to find the length of KL.
From the given statement, it is mentioned that PL is the angle bisector of ∠KPM. To find the length of KL, we can use the angle bisector theorem.
The angle bisector theorem states that in a triangle, the angle bisector divides the opposite side into segments that are proportional to the lengths of the other two sides.
In this case, we can use the angle bisector theorem in triangle KPM. Let's assume that KL represents the length of KP and LM represents the length of PM.
According to the angle bisector theorem, we have:
KP / LM = PK / PM
Since PL is the angle bisector, we have:
KP / LM = PK / PM
By cross multiplication, we get:
KP * PM = PK * LM
So, to find the length of KL, we need to know the lengths of KP and LM. If those lengths are provided in the question or elsewhere in the given information, you can substitute those values into the equation.
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