Unit 1
... Two figures are similar if and only if there is a sequence of similarity transformations that maps one figure onto the other. Example 11: Prove that the circles are similar by identifying a sequence of similarity transformations that will map one circle onto the other. ...
... Two figures are similar if and only if there is a sequence of similarity transformations that maps one figure onto the other. Example 11: Prove that the circles are similar by identifying a sequence of similarity transformations that will map one circle onto the other. ...
GEOMETRY SYLLABUS Geometry Unit Descriptions Mathematical
... defined and used to illustrate the concept of supplementary angles. The vertical angle theorem is then introduced and a proof given. The perpendicular postulate is presented and illustrated using a compass and straightedge construction. Important results about perpendicular angles are proven and use ...
... defined and used to illustrate the concept of supplementary angles. The vertical angle theorem is then introduced and a proof given. The perpendicular postulate is presented and illustrated using a compass and straightedge construction. Important results about perpendicular angles are proven and use ...
Midterm Review - Oregon State University
... Corollary: Given a line and a point P not on , there is at least one line through P to . Corollary: If 2 lines are intersected by a transversal such that a pair of corresponding s are , then the lines are . Corollary: If 2 lines are intersected by a transversal such that a pair of interio ...
... Corollary: Given a line and a point P not on , there is at least one line through P to . Corollary: If 2 lines are intersected by a transversal such that a pair of corresponding s are , then the lines are . Corollary: If 2 lines are intersected by a transversal such that a pair of interio ...
symmetry-year-2-the-woods - Pembrokeshire Outdoor Schools
... Teacher to use a stick as a line of symmetry and pebbles, and make matching or non-matching patterns either side and ask group if they are symmetrical or not. Provide each child with a flattened circle of clay and ask them to mark out a line of symmetry (with a stick, leaves pebbles etc.). Onc ...
... Teacher to use a stick as a line of symmetry and pebbles, and make matching or non-matching patterns either side and ask group if they are symmetrical or not. Provide each child with a flattened circle of clay and ask them to mark out a line of symmetry (with a stick, leaves pebbles etc.). Onc ...
5.3 Notes
... Angle-Angle-Side Congruence Theorem (AAS): If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of a second triangle, then the two triangles are congruent. If O A , and W N , and OB AM , then BOW MAN . ...
... Angle-Angle-Side Congruence Theorem (AAS): If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of a second triangle, then the two triangles are congruent. If O A , and W N , and OB AM , then BOW MAN . ...
angle
... Draw AX ^ BC, then … ABX @ ACX, by HL (AAS) Theorem and BX @ CX by CPCTC, \ AX is the ^ -bisector of BC. ...
... Draw AX ^ BC, then … ABX @ ACX, by HL (AAS) Theorem and BX @ CX by CPCTC, \ AX is the ^ -bisector of BC. ...
Triangle congruence and similarity
... straightedge. Work with these tools is powerful in developing students’ visual sense and logic, and is a strong preparation for the proofs presented in this article. In our view, the main purpose of teaching geometry in high school is to teach geometry, not to build a formal axiomatic system. The g ...
... straightedge. Work with these tools is powerful in developing students’ visual sense and logic, and is a strong preparation for the proofs presented in this article. In our view, the main purpose of teaching geometry in high school is to teach geometry, not to build a formal axiomatic system. The g ...
Lecture 17.LinearMom..
... 3180 kg is traveling in outer space with a velocity of 115 m/s. To alter its course by 35.0°, its rockets can be fired briefly in a direction perpendicular to its original motion. If the rocket gases are expelled at a speed of 1750 m/s, how much mass must be expelled? ...
... 3180 kg is traveling in outer space with a velocity of 115 m/s. To alter its course by 35.0°, its rockets can be fired briefly in a direction perpendicular to its original motion. If the rocket gases are expelled at a speed of 1750 m/s, how much mass must be expelled? ...
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.