Circle theorems - Cambridge University Press
... 5 PQ is a variable chord of the smaller of two fixed concentric circles. PQ produced meets the circumference of the larger circle at R. Prove that the product RP.RQ is constant for all positions and lengths of PQ. 6 ABC is an isosceles triangle with AB = AC. A line through A meets BC at D and the ci ...
... 5 PQ is a variable chord of the smaller of two fixed concentric circles. PQ produced meets the circumference of the larger circle at R. Prove that the product RP.RQ is constant for all positions and lengths of PQ. 6 ABC is an isosceles triangle with AB = AC. A line through A meets BC at D and the ci ...
4.1: Congruent Figures Congruent Polygons: Corresponding Angles
... Corresponding Angles: Corresponding Sides: Congruence Statement: Naming Polygons: 1) List the vertices by starting at one and working around (the corners of the figure) 2) If it’s a triangle use a small triangle in front of the vertices, for anything else, just use the word polygon Example: CAT ...
... Corresponding Angles: Corresponding Sides: Congruence Statement: Naming Polygons: 1) List the vertices by starting at one and working around (the corners of the figure) 2) If it’s a triangle use a small triangle in front of the vertices, for anything else, just use the word polygon Example: CAT ...
Unit 6: Patterns in Shape
... angle measures to create congruent triangles and quadrilaterals. Investigate properties of these figures by experimentation and by careful reasoning. Use those properties to study the design of structures and mechanisms and to solve problems. ...
... angle measures to create congruent triangles and quadrilaterals. Investigate properties of these figures by experimentation and by careful reasoning. Use those properties to study the design of structures and mechanisms and to solve problems. ...
Postulates and Theorems
... If a triangle inscribed in a circle is a right triangle, then the hypotenuse is a diameter of the circle. If a side of a triangle inscribed in a circle is a diameter of the circle, then the triangle is a right triangle. (p. 615) ...
... If a triangle inscribed in a circle is a right triangle, then the hypotenuse is a diameter of the circle. If a side of a triangle inscribed in a circle is a diameter of the circle, then the triangle is a right triangle. (p. 615) ...
On The Flat-Foldability Of A Crease Pattern
... as to the Kawasaki’s condition at v. Moreover if ϕ is a folding map for C , then we will refer to equation (1) as to the Maekawa’s condition at v. Notice that Kawasaki and Maekawa’s conditions are still necessary in the case of a crease pattern with more vertices, but in general they are not suffici ...
... as to the Kawasaki’s condition at v. Moreover if ϕ is a folding map for C , then we will refer to equation (1) as to the Maekawa’s condition at v. Notice that Kawasaki and Maekawa’s conditions are still necessary in the case of a crease pattern with more vertices, but in general they are not suffici ...
x = y
... Five ways to prove a Quadrilateral is a Parallelogram 1. Show that both pairs of opposite sides parallel 2. Show that both pairs of opposite sides congruent 3. Show that one pair of opposite sides are both congruent and parallel 4. Show that both pairs of opposite angles congruent ...
... Five ways to prove a Quadrilateral is a Parallelogram 1. Show that both pairs of opposite sides parallel 2. Show that both pairs of opposite sides congruent 3. Show that one pair of opposite sides are both congruent and parallel 4. Show that both pairs of opposite angles congruent ...
Chapter 7
... mutual bending or inclination of the planes, which is to be measured with the help of the plane angles which comprise the solid angle. For the part by which the sum of all the plane angles forming a solid angle is less than the four right angles which form a plane, designates the exterior solid angl ...
... mutual bending or inclination of the planes, which is to be measured with the help of the plane angles which comprise the solid angle. For the part by which the sum of all the plane angles forming a solid angle is less than the four right angles which form a plane, designates the exterior solid angl ...
7.2 Isosceles and Equilateral Triangles
... Use a straightedge. Draw a line. Draw an acute angle with vertex A along the line. Then use a compass to copy the angle. Place the compass point at another point B along the line and draw the copied angle so that the angle faces the original angle. Label the intersection of the angle sides as point ...
... Use a straightedge. Draw a line. Draw an acute angle with vertex A along the line. Then use a compass to copy the angle. Place the compass point at another point B along the line and draw the copied angle so that the angle faces the original angle. Label the intersection of the angle sides as point ...
Inscribed Angles and Polygons 10.4
... How are inscribed angles related to their intercepted arcs? How are the angles of an inscribed quadrilateral related to each other? An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords of the circle. An arc that lies between two lines, rays, or segments is called ...
... How are inscribed angles related to their intercepted arcs? How are the angles of an inscribed quadrilateral related to each other? An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords of the circle. An arc that lies between two lines, rays, or segments is called ...
Steinitz's theorem
In polyhedral combinatorics, a branch of mathematics, Steinitz's theorem is a characterization of the undirected graphs formed by the edges and vertices of three-dimensional convex polyhedra: they are exactly the (simple) 3-vertex-connected planar graphs (with at least four vertices). That is, every convex polyhedron forms a 3-connected planar graph, and every 3-connected planar graph can be represented as the graph of a convex polyhedron. For this reason, the 3-connected planar graphs are also known as polyhedral graphs. Steinitz's theorem is named after Ernst Steinitz, who submitted its first proof for publication in 1916. Branko Grünbaum has called this theorem “the most important and deepest known result on 3-polytopes.”The name ""Steinitz's theorem"" has also been applied to other results of Steinitz: the Steinitz exchange lemma implying that each basis of a vector space has the same number of vectors, the theorem that if the convex hull of a point set contains a unit sphere, then the convex hull of a finite subset of the point contains a smaller concentric sphere, and Steinitz's vectorial generalization of the Riemann series theorem on the rearrangements of conditionally convergent series.↑ ↑ 2.0 2.1 ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑