1. 1. (Absolute Geometry) Assume points A, D, C, B satisfy A-D-C and B is not...
1. 1. (Absolute Geometry) Assume points A, D, C, B satisfy A-D-C and B is not on the line determined by A, D, C. Prove Internal Angle Sum of triangle ACB is less than or equal to Internal Angle Sum of triangle ADB. (NOTE: This is not Euclidean Geometry. Prove this in Absolute Geometry.)
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1. 1. (Absolute Geometry) Assume points A, D, C, B satisfy A-D-C
and B is not...
(1) Assume the axioms of metric geometry. Let A, B, C, D be distinct collinear points....
(1) Assume the axioms of metric geometry. Let A, B, C, D be
distinct collinear points. Let f : l → R be a coordinate function
for the line l that crosses all of A, B, C, D. Suppose f(A) <
f(B) < f(C) < f(D). Prove that AD = AB ∪ BC ∪ CD. (2) Assume
the axioms of metric geometry. Let A, B, C, D be distinct collinear
points. Suppose A ∗ B ∗ C and B ∗...
Prove that (P;L; d) not satisfy postulate 6 of neutral geometry L = {1 c R313(a,b,c.),...
Prove that (P;L; d) not satisfy postulate 6 of neutral geometry
L = {1 c R313(a,b,c.), (u, v, w) є R3, such that I = {(a, b, cht.(u, v, w)|t є R)), and d: Px PR U, V, W T22 Postulate 6 (The Plane Separation Postulate). For any line l, the set of all points not on l is the union of two disjoint subsets called the sides ofl. If A and B are distinct points not on t, then...
extensive detail please and asap Problem 2 (10 points) (a) In Euclidean geometry explain why the...
extensive detail please and asap
Problem 2 (10 points) (a) In Euclidean geometry explain why the sum of the angles of a triangle equals two right angle. (b) In spherical geometry, what can you say about the sum of the angles of a spherical triangle?
8. True or false (in absolute geometry unless otherwise stated.) (a) If A and D are...
8. True or false (in absolute geometry unless otherwise stated.) (a) If A and D are points on opposite sides of BC and LABC BCD, then AB II CD (b) If two lines are parallel, then they are equidistant from each other. (c) If oABCD is a quadrilateral with right angles at A, B, and C, then LD is also a right angle. (d) Euclid's Parallel Postulate is equivalent to the following statement: Every point in the interior of an...
Part III (3 pts) For cach of the property statement below, determine which geometry would BEST xhoi given property (choose only one!). Please use A. for Euclidean geometry, B. for hypere geometry...
Part III (3 pts) For cach of the property statement below, determine which geometry would BEST xhoi given property (choose only one!). Please use A. for Euclidean geometry, B. for hypere geometry, gcometry and D. for Neutral geometry for your identifications Example. A There is a triangle in which the sum of the measures of the interior angles is 180. a. The opposite sides of a parallelogram are congruent. b. Similar triangles may not be congruent. Lines perpendicular to the...
2) (i) State the converse of the Alternate Interior Angle Theorem in Neutral Geometry. (ii) Prove...
2) (i) State the converse of the Alternate Interior Angle Theorem in Neutral Geometry. (ii) Prove that if the converse of the Alternate Interior Angle Theorem is true, then all triangles have zero defect. [Hint: For an arbitrary triangle, ABC, draw a line through C parallel to side AB. Justify why you can do this.] 5) Consider the following statements: I: If two triangles are congruent, then they have equal defect. II: If two triangles are similar, then they have...
3 nat you ho has cheated on this exam. 1. Let AABN and AA'B'Y by asymptotic...
3
nat you ho has cheated on this exam. 1. Let AABN and AA'B'Y by asymptotic triangles. Prove that if LABN 2 ZA'B'Y and AB> ΑΒ , then /BAΩ< ΒA. 2. Let AABC be an ordinary triangle and let D be any point of the interior. Prove that the sum of the angles of AABD is greater than the sum of the angles of AABC. 3. Suppose that two lines & and m have a common perpendicular MN. Let A...
9. ( 20 points.) In the Cartesian plane model of Euclidean geometry, which of the triples...
9. ( 20 points.) In the Cartesian plane model of Euclidean geometry, which of the triples of points (a)-(d) below, if any, are the vertices of a right triangle? (a) (2, 1), (7,0),(5, 7). (b) (102,51), (101, 48), (105,57). (e) (2,1),(4,0),(4,7). (d) (102. - 49), (104,-50). (105,-43). (c) None
3. Consider a geometry with five points a, b, c, d, and e. Let the lines...
3. Consider a geometry with five points a, b, c, d, and e. Let the lines consist of sets of two points. There are ten lines in this geometry. Show that, for every point P not on a line 1, there are at least two lines parallel to l.
Using the notation of the lecture note, assume that the means satisfy the condition that μ-m + (b-1)d-μ2-d . . .-μ,-d....
Using the notation of the lecture note, assume that the means satisfy the condition that μ-m + (b-1)d-μ2-d . . .-μ,-d. Let independent random samples of size a be taken from the b normal distributions with common unknown variance σ2. Show that the MLE of μ and d are μ = X and
Using the notation of the lecture note, assume that the means satisfy the condition that μ-m + (b-1)d-μ2-d . . .-μ,-d. Let independent random samples of size...
(1) Assume the axioms of metric geometry. Let A, B, C, D be
distinct collinear points. Let f : l → R be a coordinate function
for the line l that crosses all of A, B, C, D. Suppose f(A) <
f(B) < f(C) < f(D). Prove that AD = AB ∪ BC ∪ CD. (2) Assume
the axioms of metric geometry. Let A, B, C, D be distinct collinear
points. Suppose A ∗ B ∗ C and B ∗...
Prove that (P;L; d) not satisfy postulate 6 of neutral geometry
L = {1 c R313(a,b,c.), (u, v, w) є R3, such that I = {(a, b, cht.(u, v, w)|t є R)), and d: Px PR U, V, W T22 Postulate 6 (The Plane Separation Postulate). For any line l, the set of all points not on l is the union of two disjoint subsets called the sides ofl. If A and B are distinct points not on t, then...
extensive detail please and asap
Problem 2 (10 points) (a) In Euclidean geometry explain why the sum of the angles of a triangle equals two right angle. (b) In spherical geometry, what can you say about the sum of the angles of a spherical triangle?
8. True or false (in absolute geometry unless otherwise stated.) (a) If A and D are points on opposite sides of BC and LABC BCD, then AB II CD (b) If two lines are parallel, then they are equidistant from each other. (c) If oABCD is a quadrilateral with right angles at A, B, and C, then LD is also a right angle. (d) Euclid's Parallel Postulate is equivalent to the following statement: Every point in the interior of an...
Part III (3 pts) For cach of the property statement below, determine which geometry would BEST xhoi given property (choose only one!). Please use A. for Euclidean geometry, B. for hypere geometry, gcometry and D. for Neutral geometry for your identifications Example. A There is a triangle in which the sum of the measures of the interior angles is 180. a. The opposite sides of a parallelogram are congruent. b. Similar triangles may not be congruent. Lines perpendicular to the...
3
nat you ho has cheated on this exam. 1. Let AABN and AA'B'Y by asymptotic triangles. Prove that if LABN 2 ZA'B'Y and AB> ΑΒ , then /BAΩ< ΒA. 2. Let AABC be an ordinary triangle and let D be any point of the interior. Prove that the sum of the angles of AABD is greater than the sum of the angles of AABC. 3. Suppose that two lines & and m have a common perpendicular MN. Let A...
9. ( 20 points.) In the Cartesian plane model of Euclidean geometry, which of the triples of points (a)-(d) below, if any, are the vertices of a right triangle? (a) (2, 1), (7,0),(5, 7). (b) (102,51), (101, 48), (105,57). (e) (2,1),(4,0),(4,7). (d) (102. - 49), (104,-50). (105,-43). (c) None
3. Consider a geometry with five points a, b, c, d, and e. Let the lines consist of sets of two points. There are ten lines in this geometry. Show that, for every point P not on a line 1, there are at least two lines parallel to l.
Using the notation of the lecture note, assume that the means satisfy the condition that μ-m + (b-1)d-μ2-d . . .-μ,-d. Let independent random samples of size a be taken from the b normal distributions with common unknown variance σ2. Show that the MLE of μ and d are μ = X and
Using the notation of the lecture note, assume that the means satisfy the condition that μ-m + (b-1)d-μ2-d . . .-μ,-d. Let independent random samples of size...
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