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roneesmith2016
30.07.2019 •
Mathematics
Given: klmn is a parallelogram, ka − angle bisector of ∠k la − angle bisector of ∠l prove: m∠kal = 90°
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Ответ:
m∠NKL + m∠KLM = 180°
by reason
consecutive angles of parallelogram supplementary
Step-by-step explanation:
i just finished my rsm, if anybody is looking for the answer this is correct guaranteed :)
Ответ:
Parallelogram KLMN (see diagram) has KL parallel to NM. We are asked about angle KAL so le's call its measure z.
KA bisents angle K which means that it cuts it into two equal parts. As a result angle LKA and angle NKA are equal in measure. I call the measure of each of these x.
LA bisects angle L so it cuts angle L into two equal parts. That is, angle KLM and angle ALM are equal in measure. I call the measure of each y.
Triangle KLA contains angles measuring x, y and z. Since it is a triangle the sum of its interior angles is 180 degrees. That means x + y + z = 180.
In a parallelogram the consecutive angles sum to 180 degrees.
If you want to know why this is true it is because KN and LM are parallel (opposite sides of a parallelogram) and KL is a transversal (cuts through the parallel lines - it might help to extend KN and LM to see this better and also to turn your paper so that LM is at top). Angles K and L are interior angles on the same side of the transversal and so sum to 180 degrees.
The above means that angles K and L sum to 180 degrees. So, x + x + y + y = 180. That is 2x + 2y = 180 and 2(x+y) = 180 so x+y = 90 degrees.
from before we know that x + y + z = 180 degrees. Since we know that x + y = 90 degrees that means 90 + z = 180 so z = 90 degrees.
As such we have just shown that angle KAL measures 90 degrees as asked.
Ответ: