2.) Which is true about both Pappus's Theorem and Desargues' Theorem?
Each theorem applies to spherical geometry.
Each conclusion states that three points are collinear. <----
Each hypothesis is based on triangles.
Each theorem involves a dilation.
3.) How many degrees are in the sum of the angle measures in a spherical triangle?
180° <----
360°
between 180° and 540°
between 360° and 540°
4.) What is the taxidistance between (1, 4) and (12, 6)?
13 <-------
15
21
23
5.) Which dimensions are closest to those of a golden rectangle?
0.5 × 1.6
1 × 3.24
7 × 11.33 <----
17 × 25.5
6. Which is true about taxicab geometry?
Taxicab geometry is measured in the coordinate plane and therefore is a branch of Euclidean geometry.
The shortest distance between two points is a straight line.
To travel a path in taxicab geometry, you can move vertically, horizontally, or diagonally on a coordinate grid. <-----
Between points A and B, there may be more than one path that shows the taxidistance.
3 is wrong. I don't know about 2.
Okay, is 3
between 180° and 540° ?
Thank you bob :)
Jazy, this is considered a form of cheating! Please get help by asking a teacher, this is against academic policy!
To answer these questions, you can rely on the information provided and apply some basic mathematical concepts. Here's how you can get the answers:
2.) The question asks which statement is true about both Pappus's Theorem and Desargues' Theorem. To determine this, you can go through each statement provided and see if it applies to both theorems. The correct answer is the one that applies to both theorems. In this case, the correct answer is "Each conclusion states that three points are collinear."
3.) The question asks how many degrees are in the sum of the angle measures in a spherical triangle. You can recall that in Euclidean geometry, the sum of angle measures in a triangle is 180 degrees. However, in spherical geometry, the sum of angle measures in a triangle is different. To find the answer, you need to remember that in spherical geometry, the sum of angle measures in a triangle is greater than 180 degrees. The correct answer is "between 180° and 540°" since this range includes all possible sums of spherical triangle angles.
4.) The question asks for the taxidistance between two given points. Taxidistance refers to the distance traveled as if one were moving through a city grid, where movement can only happen vertically, horizontally, or diagonally. To find the taxidistance between two points, you can calculate the difference in the x-coordinates and the difference in the y-coordinates of the two points. Then, add the absolute values of these differences. In this case, the taxidistance between (1, 4) and (12, 6) can be calculated as |12-1| + |6-4| = 11 + 2 = 13. The correct answer is 13.
5.) The question asks for the dimensions that are closest to those of a golden rectangle. A golden rectangle has a special aspect ratio, where the ratio of its length to its width is equal to the golden ratio, approximately 1.618. You can calculate the aspect ratio for each given option and see which one is closest to the golden ratio. In this case, the correct answer is "7 × 11.33" since its aspect ratio of 11.33/7 is closer to 1.618 compared to the other options.
6.) The question asks which statement is true about taxicab geometry. Taxicab geometry refers to a method of measuring distance in a coordinate plane where movement is restricted to vertical, horizontal, or diagonal paths. To determine the correct statement, you can go through each option and see which one accurately describes taxicab geometry. The correct answer is "To travel a path in taxicab geometry, you can move vertically, horizontally, or diagonally on a coordinate grid." This accurately describes the movement allowed in taxicab geometry.