1. If line JK is perpendicular to line XY at its midpoint M, which statement is true?

a) JX = KY
b) JX = KX
c) JM = KM
d) JX = JY

Is it c?

2. What information is needed to conclude that line EF is the bisector of ∠DEG?
a) m∠DEF = m∠DEG
b) m∠FEG = m∠DEF
c) m∠GED = m∠GEF
d) m∠DEF = m∠EFG

Is it b?

1. To determine which statement is true, we need to understand the properties of perpendicular lines and midpoints.

Perpendicular lines intersect at a right angle, which means that the angles formed are 90 degrees. In this case, line JK is perpendicular to line XY at its midpoint M.

Now, let's analyze the given statements:

a) JX = KY - There's no information about these distances in the question, so we can't conclude this statement.
b) JX = KX - This statement suggests that J and K are the same point, which is not indicated in the question.
c) JM = KM - This statement is correct. Given that M is the midpoint of XY, JM and KM will have the same length since M divides XY into two equal segments.
d) JX = JY - There's no information about JY in the question, so we can't determine if this statement is true.

Based on this reasoning, the correct answer is c) JM = KM.

2. To conclude that line EF is the bisector of ∠DEG, we need to understand what a bisector does. A bisector divides an angle into two congruent (equal) angles.

Let's analyze the given statements:

a) m∠DEF = m∠DEG - This statement only suggests that angles DEF and DEG have equal measures, but it doesn't imply that EF is the bisector. So, it is not the correct answer.
b) m∠FEG = m∠DEF - This statement indicates that angles FEG and DEF have equal measures, which suggests that EF is the bisector of ∠DEG. Therefore, this statement is correct.
c) m∠GED = m∠GEF - This statement suggests that angles GED and GEF have equal measures, which doesn't necessarily mean that EF is the bisector.
d) m∠DEF = m∠EFG - This statement only suggests that angles DEF and EFG have equal measures, but it doesn't imply that EF is the bisector. So, it is not the correct answer.

Based on this reasoning, the correct answer is b) m∠FEG = m∠DEF.

Therefore, your answers are correct!

#1 correct

But the wording makes ambiguous whether M is the midpoint of JK or XY.

#2 correct

Yass lets hit it miss bean

line JK perpendicular to line LM