I hope to know that answer for K, L, M, N from number 5 and 6. It is confusing w
ID: 2900097 • Letter: I
Question
I hope to know that answer for K, L, M, N from number 5 and 6.
It is confusing which part is related for this sentenced.
This is from Modern geometry.
5. (3 pts each) Which of the following are true in Hyperbolic space (H) Elliptical/Spherical space (S), Euclidean (E), or all of these (A). (Some may have multiple answers) Through a point not on a "line" there exists no parallel lines b. Triangles are congruent by AAA. The sum of the angles of a triangle is equal to 180 degrees Triangles can be congruent by having two pairs of congruent corresponding angles, provided the third corresponding "angle" is at infinity (AA2) The exterior angle of a triangle is equal to the sum of the two remote interior angles The area of a triangle is related to the angle sum of that triangle The summit angles of a Saccheri quadrilateral are obtuse Through a point not on a "line" there exists multiple parallels to the original line The smallest polygon is a two sided shape called a lune The remaining angle of a Lambert Quadrilateral must be acute k. Rectangles exist All right angles are congruent to each other m. Saccheri quadrilaterals exist Vertical angles are congruent. n. 6. (6 pts) Find the area of a triangle on the earth (radius 3980 mi) with angles that measure 45, 85, and 70 degreesExplanation / Answer
b. No triangle AAA means we are given all three angles of a triangle, but no sides. This is not enough information to decide if two triangles are congruent.
c.True (properties of triangle)
k.
No such rectangle exists.
Suppose you have a rectangle with mm rows and nn columns. If every row adds up to some magic value MM, then the number obtained by adding together every cell in the rectangle must be m×Mm×M.
Likewise, if every column adds up to MM, then the value obtained by adding together every cell in the rectangle must also equal n×Mn×M.
So, m×M=n×Mm×M=n×M. This can only be true if m=nm=n, which corresponds to a square.
(L).
We say that the angle AOBAOB is the supplement of the angle YY if the latter is congruent to an adjacent angle BOCBOC to AOBAOB such that the points AA, OO and CC are colineal.
Using this definition and the fact that an angle is Right iff it's congruent to one of its supplements(by definition), you can prove that all right angles are congruent as follows:
Let AOBAOB be a right angle, then it's congruent to one of its supplements (and therefore to all of them). Let BOCBOC be an adjacent supplement of AOBAOB, then AOBBOCAOBBOC and AA, 00, CC are colineal.
Now let YY be any other right angle and consider DD an exterior point of AOBAOB such that AODAODis a right angle congruent to YY. Here you have to prove that: BB, OO and DD are colineal and once you have this prove that AOBAODAOBAOD (using "vertex opposites" arguments),
(m). According to Euclid's fifth postulate
if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.
(n).If two angles are vertical angles, then they’re congruent
6. 1 mi =1.6 km