Hello. Going over a study guide for my geometry test. Came across a few issues. My book isn't much help. Mind explaining it in laymen terms/proofs? 10th grade geometry student.
Here is the first one (the one giving me the most trouble).
Here's the second one, I feel like I haven't been given enough information.
Thanks a bunch!
1. l perpendicular to n Reason: given
2. angle ABJ is a right angle Reason: definition of "perpendicular"
3. m perpendicular to n Reason: given
4. Angle DCH is a right angle Reason: definition of "perpendicular".
5. Angle ABJ is congruent to angle DCH Reason: all right angles are congruent
6. Angle ABJ is congruent to angle KHL Reason: given
7. Angle KHL is congruent to angle DCH Reason: things congruent to the same thing are congruent to each other.
That is how I would do it. Of course, I do not know exactly what "postulates" and "theorems" you have available to use. For example, it might be that you do NOT (yet) have "all right angles are congruent" but rather that "all right angles have a measure of 90 degrees" and "if two angles have the same measure they are congruent". Of you might not have "two lines are perpendicular if and only if they form right angles" but "if two lines are perpendicular, then they form four angles with measure 90 degrees".
Theorem 1 vertical angles are congruent
Practical proof. Draw intersecting lines.Cut out the angles and note they have equal measures
Line proof .Label the opposite angles of intersecting lines 1and 2 and 3 and 4 their supplements.1 and 2 are vertical
m1 +m3 = 180 additive property postulate
m2+m3 = 180 same
m1+m3 =m2+m3 equals to equals are equal to each other
m1=m2 subtract m3 from each side