7.3 - Proving Triangles Similar.notebook
... “If an angle of one triangle is congruent to an angle of a second triangle, and the sides that include the two angles are proportional then the triangles are similar.” ...
... “If an angle of one triangle is congruent to an angle of a second triangle, and the sides that include the two angles are proportional then the triangles are similar.” ...
File - Analytic Geometry
... Warm-up Begin at the word “Tomorrow”. Every Time you move, write down the word(s) upon which you land. ...
... Warm-up Begin at the word “Tomorrow”. Every Time you move, write down the word(s) upon which you land. ...
Math Extra Credit
... 2. Unique Angle Assumption: Given any ray VA (→) and any real number r between 0 and 180, there is a unique angle BVA in each half-plane of line VA (<-->) such that m
... 2. Unique Angle Assumption: Given any ray VA (→) and any real number r between 0 and 180, there is a unique angle BVA in each half-plane of line VA (<-->) such that m
On some log-cosine integrals related to (3), (4), and (6)
... Previously, a certain log-cosine integral has been considered in connection with certain digamma series [3,6]. This integral has value a rational multiple of (4), where is the Riemann zeta function [7,10,15,12]. We show that this integral may be alternatively evaluated starting from a known tabu ...
... Previously, a certain log-cosine integral has been considered in connection with certain digamma series [3,6]. This integral has value a rational multiple of (4), where is the Riemann zeta function [7,10,15,12]. We show that this integral may be alternatively evaluated starting from a known tabu ...
2-6 reteaching
... Name a pair of congruent angles in each figure. Justify your answer. 5. Given: 2 is complementary to 3. ...
... Name a pair of congruent angles in each figure. Justify your answer. 5. Given: 2 is complementary to 3. ...
Properties-of-Triangles
... The triangle angle-sum theorem states that all three angles of triangle angle- any triangle must have a sum of 180°. sum theorem? Example 1: 30°, 40°, & 110° angles can form triangles because their sum is 180° Example 2: 45°, 50°, & 90° do not form a triangle because 45 + ...
... The triangle angle-sum theorem states that all three angles of triangle angle- any triangle must have a sum of 180°. sum theorem? Example 1: 30°, 40°, & 110° angles can form triangles because their sum is 180° Example 2: 45°, 50°, & 90° do not form a triangle because 45 + ...
Proving Geometric Relationships 2.6
... ∠1 is congruent to ∠2. By the definition of congruent angles, the measure of ∠1 is equal to the measure of ∠2. The measure of ∠2 is equal to the measure of ∠1 by the Symmetric Property of Equality. Then by the definition of congruent angles, ∠2 is congruent to ∠1. ...
... ∠1 is congruent to ∠2. By the definition of congruent angles, the measure of ∠1 is equal to the measure of ∠2. The measure of ∠2 is equal to the measure of ∠1 by the Symmetric Property of Equality. Then by the definition of congruent angles, ∠2 is congruent to ∠1. ...
DIFFERENTIAL EQUATIONS ON HYPERPLANE COMPLEMENTS II Contents 1 3
... In this case, Hreg = C∗ \ {±1}, while T reg = C∗ \ {1}. The nontrivial element σ in the Weyl group Z2 acts by z 7→ z−1 in both case. It’s obvious that W action on T reg is not free, since it fixes the element −1. The fundamental group of Hreg /W is called affine Braid group, the following propositio ...
... In this case, Hreg = C∗ \ {±1}, while T reg = C∗ \ {1}. The nontrivial element σ in the Weyl group Z2 acts by z 7→ z−1 in both case. It’s obvious that W action on T reg is not free, since it fixes the element −1. The fundamental group of Hreg /W is called affine Braid group, the following propositio ...
Noether's theorem
Noether's (first) theorem states that every differentiable symmetry of the action of a physical system has a corresponding conservation law. The theorem was proven by German mathematician Emmy Noether in 1915 and published in 1918. The action of a physical system is the integral over time of a Lagrangian function (which may or may not be an integral over space of a Lagrangian density function), from which the system's behavior can be determined by the principle of least action.Noether's theorem has become a fundamental tool of modern theoretical physics and the calculus of variations. A generalization of the seminal formulations on constants of motion in Lagrangian and Hamiltonian mechanics (developed in 1788 and 1833, respectively), it does not apply to systems that cannot be modeled with a Lagrangian alone (e.g. systems with a Rayleigh dissipation function). In particular, dissipative systems with continuous symmetries need not have a corresponding conservation law.