Chapter 11 – Areas of Polygons and Circles
... Composite Figure – a figure that can be separated into different parts such as triangles, squares, rectangles, etc. You find the area of each part and then add or subtract the extra parts that are needed. 4. POOL: The dimensions of an irregularly shaped pool are shown. What is the area of the surfac ...
... Composite Figure – a figure that can be separated into different parts such as triangles, squares, rectangles, etc. You find the area of each part and then add or subtract the extra parts that are needed. 4. POOL: The dimensions of an irregularly shaped pool are shown. What is the area of the surfac ...
Chapter 11 – Area of Polygons and Circles Section 11.1
... The sum of the measures of the exterior angles of a convex polygon, one angle at each vertex, is 360°. Corollary to Thm 11.2 The measure of each exterior angle of a regular n-gon is: ...
... The sum of the measures of the exterior angles of a convex polygon, one angle at each vertex, is 360°. Corollary to Thm 11.2 The measure of each exterior angle of a regular n-gon is: ...
Angles and Area of Polygons
... (a) Take a copy of the polygons in circles. For each polygon use a straightedge to draw lines from the center to each vertex. These lines will look like spokes of a wheel. (b) Note that each polygon has been divided up into triangles. Look at the inscribed square. Inscribed means it is drawn inside ...
... (a) Take a copy of the polygons in circles. For each polygon use a straightedge to draw lines from the center to each vertex. These lines will look like spokes of a wheel. (b) Note that each polygon has been divided up into triangles. Look at the inscribed square. Inscribed means it is drawn inside ...
Geometry Lesson 6.1.notebook
... 1. Using the same formula for the sum of the angles will allow us to do this. We will be solving for n. ...
... 1. Using the same formula for the sum of the angles will allow us to do this. We will be solving for n. ...
Lecture 7
... with internal angle equal to α if and only if α ∈ [0, (n − 2)π/n). (Hint: Work in the Poincaré disc D. Let ω = e 2πi/n be an nth root of unity. Fix r ∈ (0, 1) and consider the polygon D(r) with vertices at r, rω, rω 2 , . . . , rω n−1 . This is a regular n-gon (why?). Let α(r) denote the internal a ...
... with internal angle equal to α if and only if α ∈ [0, (n − 2)π/n). (Hint: Work in the Poincaré disc D. Let ω = e 2πi/n be an nth root of unity. Fix r ∈ (0, 1) and consider the polygon D(r) with vertices at r, rω, rω 2 , . . . , rω n−1 . This is a regular n-gon (why?). Let α(r) denote the internal a ...
Combined Notes
... L5 Perimeters of Polygons Perimeter= is the total distance around an object We can find the perimeter of any polygon by adding the side lengths ...
... L5 Perimeters of Polygons Perimeter= is the total distance around an object We can find the perimeter of any polygon by adding the side lengths ...
Extensions to complex numbers
... • The conjugate of a vector v is obtained by taking the conjugate of each component in v. • The conjugate of a matrix M is obtained by taking the conjugate of each entry in M. • The Hermitian of a complex matrix M, is defined as the conjugate transpose of M. • The Hermitian of M is denoted by MH or ...
... • The conjugate of a vector v is obtained by taking the conjugate of each component in v. • The conjugate of a matrix M is obtained by taking the conjugate of each entry in M. • The Hermitian of a complex matrix M, is defined as the conjugate transpose of M. • The Hermitian of M is denoted by MH or ...
4.1 Symmetry Geometry and measures
... The shape now has rotational symmetry of order four. If you rotate the shape about the centre it will come back on itself four times in one complete revolution. You can check this with tracing paper. ...
... The shape now has rotational symmetry of order four. If you rotate the shape about the centre it will come back on itself four times in one complete revolution. You can check this with tracing paper. ...
Topology Proceedings - Topology Research Group
... (gXg-l (h l ), .. · , gXg-l (h n )) Now equivariance of J1 is obvious. To see that it is an embedding, notice that two vertices of C(f) differ iff they are separated by some mirror say in h; thus their images in Th are different.D Proof of Theorem 1 In view of Lemmas 1-3 we should only notice that t ...
... (gXg-l (h l ), .. · , gXg-l (h n )) Now equivariance of J1 is obvious. To see that it is an embedding, notice that two vertices of C(f) differ iff they are separated by some mirror say in h; thus their images in Th are different.D Proof of Theorem 1 In view of Lemmas 1-3 we should only notice that t ...
Mid-Term Review Part II
... State the postulate or theorem (SSS, SAS, ASA, AAS or HL) you can use to prove each pair of triangles congruent. If the triangles cannot be proven congruent, write not enough information. ...
... State the postulate or theorem (SSS, SAS, ASA, AAS or HL) you can use to prove each pair of triangles congruent. If the triangles cannot be proven congruent, write not enough information. ...
Quaternionic groups November 5, 2014
... the multiplication rules are determined by (0.1c). There is an algebra antiautomorphism of the quaternions given by a + bi + cj + dk = a − bi − cj − dk, ...
... the multiplication rules are determined by (0.1c). There is an algebra antiautomorphism of the quaternions given by a + bi + cj + dk = a − bi − cj − dk, ...
LESSON 4-1: CONGRUENT FIGURES/POLYGONS
... POLYGON: A polygon is a closed plane figure formed by three or more segments. Each segment intersects exactly two other segments, but only at their endpoints, and no two segments with a common endpoint are collinear. The vertices of the polygon are the endpoints of the sides. When naming a polygon, ...
... POLYGON: A polygon is a closed plane figure formed by three or more segments. Each segment intersects exactly two other segments, but only at their endpoints, and no two segments with a common endpoint are collinear. The vertices of the polygon are the endpoints of the sides. When naming a polygon, ...
Chapter 7
... Theorem 56: If one of the exterior angles is taken at each vertex, the sum SE of the measures of the exterior angles of a polygon is given by the formula S E = 360. ...
... Theorem 56: If one of the exterior angles is taken at each vertex, the sum SE of the measures of the exterior angles of a polygon is given by the formula S E = 360. ...
Investigate Angle Sums in Polygons
... Investigate Angle Sums in Polygons M AT E R I A L S • straightedge • ruler ...
... Investigate Angle Sums in Polygons M AT E R I A L S • straightedge • ruler ...
Name: Answer Key Period ______ 1st Semester Exam Review
... a. If MATH is reflected across the line y = -x and then translated 2 units down to become parallelogram M AT H , what will be the coordinates of M ? (-5, -5) b. What transformation(s) created an image with a vertex at (3,0)? (x +1, y -1) c. Rotate MATH 90° clockwise about the origin. M’(5, -3 ...
... a. If MATH is reflected across the line y = -x and then translated 2 units down to become parallelogram M AT H , what will be the coordinates of M ? (-5, -5) b. What transformation(s) created an image with a vertex at (3,0)? (x +1, y -1) c. Rotate MATH 90° clockwise about the origin. M’(5, -3 ...
Answers for the lesson “Classify Polygons”
... 33x 1 9. Since x 5 3, the measure of an angle of the pentagon is 1088. ABC and ACB form a linear pair with an angle of a pentagon so they are both equal to 1808 2 1088 5 728. BAC, CAD, and DAE must have a sum of 1808. Since CAB > DAE, 2y 1 108 5 180, y 5 36, so m CAB 5 368. Problem So ...
... 33x 1 9. Since x 5 3, the measure of an angle of the pentagon is 1088. ABC and ACB form a linear pair with an angle of a pentagon so they are both equal to 1808 2 1088 5 728. BAC, CAD, and DAE must have a sum of 1808. Since CAB > DAE, 2y 1 108 5 180, y 5 36, so m CAB 5 368. Problem So ...
Topics in Graph Theory — Lecture Notes I (Tuesday)
... loop. Two edges e, e0 are allowed to have the same pairs of endpoints; such edges are called parallel. Unless otherwise specified, all graphs are undirected—if the endpoints of e are v and w, we will write e = vw = wv. If v and w are adjacent (that is, they share at least one edge), then we’ll write ...
... loop. Two edges e, e0 are allowed to have the same pairs of endpoints; such edges are called parallel. Unless otherwise specified, all graphs are undirected—if the endpoints of e are v and w, we will write e = vw = wv. If v and w are adjacent (that is, they share at least one edge), then we’ll write ...
Geometry Summer Packet: 2015
... When reading a diagram: Things you may assume: 1. You may assume that lines are straight, and if two lines intersect, they intersect at one point. 2. You may assume that points on a line are collinear and that all points shown in a diagram are coplanar unless planes are drawn to show that they are n ...
... When reading a diagram: Things you may assume: 1. You may assume that lines are straight, and if two lines intersect, they intersect at one point. 2. You may assume that points on a line are collinear and that all points shown in a diagram are coplanar unless planes are drawn to show that they are n ...
1.11 Curriculum Framework
... Describe triangles, squares, and rectangles by the number of sides, vertices, and angles. (a) Recognize that rectangles and squares have special types of angles called right angles. (a) Sort plane figures based on their characteristics (number of sides, vertices, angles, curved, etc.). (a) Identify ...
... Describe triangles, squares, and rectangles by the number of sides, vertices, and angles. (a) Recognize that rectangles and squares have special types of angles called right angles. (a) Sort plane figures based on their characteristics (number of sides, vertices, angles, curved, etc.). (a) Identify ...
North Thurston Public Schools Geometry 3 rd Quarter Review Booklet
... 12. An n-gon has interior angles which sum up to 2700°. How many sides does the n-gon have? ...
... 12. An n-gon has interior angles which sum up to 2700°. How many sides does the n-gon have? ...
Unit 4 - CEISMC
... Look for graphs and charts in newspapers and magazines. Collect them and help your child organize them by type of graph. Ask your child to categorize containers in your household by geometric shapes. Look for cans, boxes, cups, and cones. Discuss how they are alike and how they are different. Count ...
... Look for graphs and charts in newspapers and magazines. Collect them and help your child organize them by type of graph. Ask your child to categorize containers in your household by geometric shapes. Look for cans, boxes, cups, and cones. Discuss how they are alike and how they are different. Count ...
Math 319 Problem Set 3: Complex numbers and Quaternions Lie
... v = (v1 , . . . , vn ) is v = (v1 , . . . , vn ).) Complex conjugation has a simple relationship to matrix operations on A, B ∈ M(n, C). For each of the following, you may make your argument for the case when n = 2, but to make the generalization to arbitrary n easier later, write your two by two ma ...
... v = (v1 , . . . , vn ) is v = (v1 , . . . , vn ).) Complex conjugation has a simple relationship to matrix operations on A, B ∈ M(n, C). For each of the following, you may make your argument for the case when n = 2, but to make the generalization to arbitrary n easier later, write your two by two ma ...
Complex polytope
In geometry, a complex polytope is a generalization of a polytope in real space to an analogous structure in a complex Hilbert space, where each real dimension is accompanied by an imaginary one. On a real line, two points bound a segment. This defines an edge with two bounding vertices. For a real polytope it is not possible to have a third vertex associated with an edge because one of them would then lie between the other two. On the complex line, which may be represented as an Argand diagram, points are not ordered and there is no idea of ""between"", so more than two vertex points may be associated with a given edge. Also, a real polygon has just two sides at each vertex, such that the boundary forms a closed loop. A real polyhedron has two faces at each edge such that the boundary forms a closed surface. A polychoron has two cells at each wall, and so on. These loops and surfaces have no analogy in complex spaces, for example a set of complex lines and points may form a closed chain of connections, but this chain does not bound a polygon. Thus, more than two elements meeting in one place may be allowed.Since bounding does not occur, we cannot think of a complex edge as a line segment, but as the whole line. Similarly, we cannot think of a bounded polygonal face but must accept the whole plane.Thus, a complex polytope may be understood as an arrangement of connected points, lines, planes and so on, where every point is the junction of multiple lines, every line of multiple planes, and so on. Likewise, each line must contain multiple points, each plane multiple lines, and so on.