Raj correctly determined that ray LH is the bisector of AngleGLI.
A line contains points K, L, M. 4 lines extend from point L. One line extends to point F, another to G, another to H, and another to I.
Which information could he have used to determine this?
AngleGLH Is-congruent-to AngleILM
mAngleKLM = 5mAngleILM
mAngleGLI = 2mAngleGLH
mAngleGLI = mAngleGLH + mAngleHLI
Answers
Answer: option 3) m∠GLI = 2m∠GLH
Step-by-step explanation:
According to the question, let us draw a line segment with points K, L & M.
Then let point L is extended to point F, point G, point H & finally to point I (as shown in the figure attached below)
We are also given that Raj determines LH being the angle bisector of GLI by using one of the options given in the question.
Now, let's find out which of the options may have helped him to determine, LH is the bisector of ∠GLI, by studying each of the options separately:
i) ∠GLH Is-congruent-to ∠ILM
From the figure, we can see that LH is a ray which lies between the angle GLI. So, AngleGLH being congruent to AngleILM does not help us to determine that LH is an angle bisector.
∴ option (i) is incorrect
ii) m∠KLM = 5m∠ILM
K, L & M is a line segment. So, ∠KLM is a straight angle. Since all the other angles are located on the line KLM, therefore, we can say that
m∠KLM = m∠KLF + m∠FLG + m∠GLH + m∠HLI + m∠ILM = 5m∠ILM
But this option also does not tell us that LH is an angle bisector.
∴ option (ii) is incorrect
iii) m∠GLI = 2m∠GLH
We know from the figure,
m∠GLI = m∠GLH + m∠HLI
from the option (iii) given we can conclude m∠GLH = m∠HLI
∴ ray LH bisects ∠GLI into two equal angles GLH & HLI.
∴ option (iii) is correct
iv) m∠GLI = m∠GLH + m∠HLI
From the figure we can see that, m∠GLI = m∠GLH + m∠HLI but no other information is given about the relation between the ∠GLH & ∠HLI.
∴ option (iv) is incorrect
Answer:
Step-by-step explanation:
The answer is fairly simple it is C I just took the test and i saw the correct answers for all of them on edge and this one appears to be C.