true or false. geometry question corresponding angles postulates?
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the second proposition is a formulation of Euclid's postulate of the paralleles.\nIt's precisely a postulate, as the same Euclid posed it; rinascimental mathematicians tried to prove it as a theorem, but they failed: in fact Euclid knew well what he was doing.\nThe postulate of the paralleles defines the Euclidean geometry, which is "platonic": it needs abstraction, because you can't apply it on the spherical surface of the Earth.\n\nSo the answer to your first question is no: if you assume spherical geometry, and thus parallels as maximum circles on the sphere, the angles postulate doesn't work anymore.\n\n(Notice that ancient Greeks were able to measure the Earth's radius by astronomycal calculations: so they knew very well how the Earth was not planar ... )
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Statements\n1) PT tangent to circle O, PAB is a secant.\nReason: Given\n2)Draw line TB\nreason: two points determine a line\n3) angle mtp is congruent to angle mtb\nreason: an angle bisector(line MT) bisects an angle into two congruent angles\n4) draw tangent XY that meets at point T and is parallel to line segment PB\nreason: a tangent may be drawn to one point of a circle\n5) angle mtb is congruent to angle pmt \nreason: when a transversal crosses two parallel lines the alternate interior angle formed are congruent\n6) angle mtp is congruent to angle pmt\nreason: i forgot the name of this theorom look it up(something like if x=y and y=z then x=z)\n7) triangle PMT is isoceles \nreason= converse of the base angles theorm\n\ni hope i was able to help somewhat, i tried to draw a diagram to the best of my ability with the given information. by the way i know there was another way to do the proff with circle properties but i think it was much easier to draw a tangent parallel to PB saved a lot of steps also. good luck!
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90\n\nA pair of angles are complementary if the sum of their measures is 90 degrees.\n\nIf the two complementary angles are adjacent (i.e. have a common vertex and share a side, but do not have any interior points in common) their non-shared sides form a right angle.
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If I told you, you would get the answer correct, but would not have learned your trig assignment.\n\nHint:  Those tables in the back of the book are there for a reason!
42171
A fact is that the world is round (it can be proved). An opinion is the world is flat (a statement that can be proved wrong).
661088
If the sides are parallel then these angles will be equal.
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Well I'm not a geometer ... so I may err slightly here as i only had one non-euclidean geometry class and going over some links has only refreshed some of it.\n\nRiemannian geometry is otherwise known as elliptic geometry :\n"It can be visualized as the surface of a sphere on which "lines" are taken as great circles. In elliptic geometry, the sum of angles of a triangle is > 180 degrees"  [this last part taken from mathworld]. It is a "non-euclidean" geometry "with positive curvature" which replaces the "parallel postulate" with *through any point in the plane, there exist no lines parallel to a given line.*\n\ntaken from wikipedia :\nSpherical trigonometry is a part of spherical geometry that deals with polygons (especially triangles) on the sphere and explains how to find relations between the involved angles. This is of great importance for calculations in astronomy and earth-surface and orbital and space navigation.\n\nSo one could say ... paraphrase the above defn of spherical trigonometry mentioning how it is a study of the relations of polygons, angles etc on objects under (or in) a riemannian geometry system\n\nincluded below are some of the links so you can formulate a better answer than mine :) gain a better understanding and even give examples that you find in those links and related links :)\n\nenjoy :),\nTom
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For indirect proofs you start with the opposite of the conclusion.\nIn this case, you take the opposite of "the angles opposite those sides are not congruent" and make it "the angles opposite those sides are congruent".  Therefore, two sides of a triangle are congruent since if the base angles are congruent, the sides are congruent.  Then you state it's a contradiction because it contradicts the given fact that the two sides of a triangle are not congruent.  Then you just say therefore, our assumption is incorrect and the angles opposite those sides are not congruent.
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1. True. \n2. True.\n3. True.\n4. False. A parallelogram has no symmetry at all.\n5. True.
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It's true!\nThat's right, it's true that this question is actually false! Since you asked if it was false, the answer would be true!!\nGot it?! ;0)
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1.  When two lines cross, pairs of vertical angles are congruent.\n\n2. If two parallel lines are cut by a transbersal, alternate interior angles formed are congruent.\n\n3. If two parallel lines are cut by a transbersal, alternate exterior angles formed are congruent.\n\n4. If two parallel lines are cut by a transbersal, corresponding angles formed are congruent.\n\n5.  Opposite angles of a parallelogram are congruent.\n\n6. Base angles of an isosceles triangle or trapezoid are congruent.\n\n7. Perpendicular lines meet to form congruent angles.\n\n8.  If two angles are both congruent to a third angle, they are congruent to each other.\n\n9.  A pair of right angles are congruent. \n\n10.  Any two angles of an equilateral triangle are congruent.\n\nThere are more but most are variations of the above.
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A pair of angles are supplementary if their respective measures sum to 180 degrees.\n\nYou would subtract an angle less than 180 to get it's supplement.
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by the number of sides and angles
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I think right angles are, because we just did that in my class and thats what i heared. good luck
1017007
Ive noticed you were asking quite alot of these geometry questions. I think you should pay more attention in class and you wouldnt need to ask home work questions, and plus, just knowing the answer wont help, youll have to know how to do it, especially if this is for a final exam...
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the question really should be, 'which direction is the earth spinning if you look at it from (insert place here)?'\n\nit all depends on your frame of reference. and your direction of reference. and your size of reference.
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|\n  | \n  |  A\n  |\n  |_______\n......B\n\nThis is what "A" perpendicular to "B" looks like.  I hope this helps!