0035_hsm11gmtr_0904.indd
... sketch the line(s) of symmetry. If it has rotational symmetry, tell the angle of rotation. 1. To start, look for the ways that the figure will reflect ...
... sketch the line(s) of symmetry. If it has rotational symmetry, tell the angle of rotation. 1. To start, look for the ways that the figure will reflect ...
Similar Triangles Lesson and Project
... Prove these two theorems by first proving that ∆ABC is similar to ∆P BA which is also similar to ∆P AC. When drawing the diagrams for the proofs, it is best to make length AC about twice the length AB so that it is easy to see which sides and angles correspond. This proof of Pythagoras as well as ot ...
... Prove these two theorems by first proving that ∆ABC is similar to ∆P BA which is also similar to ∆P AC. When drawing the diagrams for the proofs, it is best to make length AC about twice the length AB so that it is easy to see which sides and angles correspond. This proof of Pythagoras as well as ot ...
Lesson 6-2 (1)
... If a triangle has two congruent sides, then the angles opposite them are congruent. Equilateral Triangle Symmetry Theorem Every equilateral triangle has three symmetry lines, which are bisectors of its angles (or equivalently, the perpendicular bisectors of the sides). Equilateral Triangle Angle The ...
... If a triangle has two congruent sides, then the angles opposite them are congruent. Equilateral Triangle Symmetry Theorem Every equilateral triangle has three symmetry lines, which are bisectors of its angles (or equivalently, the perpendicular bisectors of the sides). Equilateral Triangle Angle The ...
Triangles and Angles
... An interior angle is formed by two sides of a triangle. An exterior angle is formed by one side of the triangle and extension of an adjacent side. ...
... An interior angle is formed by two sides of a triangle. An exterior angle is formed by one side of the triangle and extension of an adjacent side. ...
Proving Triangle Congruence by ASA and AAS
... EXPLORATION: Determining Valid Congruence Theorems Go to BigIdeasMath.com for an interactive tool to investigate this exploration. Work with a partner. Use dynamic geometry software to determine which of the following are valid triangle congruence theorems. For those that are not valid, write a coun ...
... EXPLORATION: Determining Valid Congruence Theorems Go to BigIdeasMath.com for an interactive tool to investigate this exploration. Work with a partner. Use dynamic geometry software to determine which of the following are valid triangle congruence theorems. For those that are not valid, write a coun ...
Geometry
... At this station, you will find a pair of scissors, a ruler, and a piece of paper for each group member. Each person should complete the activity and discuss his or her findings with the group. Draw a right triangle. Now draw squares using each side of the triangle as one side of the squares. There s ...
... At this station, you will find a pair of scissors, a ruler, and a piece of paper for each group member. Each person should complete the activity and discuss his or her findings with the group. Draw a right triangle. Now draw squares using each side of the triangle as one side of the squares. There s ...
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.