cond, bicond, ded and algebra
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... Images are copyright of, and used with permission from Clipart.com, © [2010], Jupiterimages Corporation, a wholly owned subsidiary of Jupiter media Corporation. All rights reserved. ...
Name: TP: ______ Unit 1 – Quadratics 1. Graph the following
... No lines must be parallel Cannot be determined from the given information ...
... No lines must be parallel Cannot be determined from the given information ...
Angles of a Triangle
... 3) After marking all of the angles, tear the triangle into three pieces. then rotate them, laying the marked angles next to each other. 4) Make a conjecture about the sum of the angle measures of the triangle. ...
... 3) After marking all of the angles, tear the triangle into three pieces. then rotate them, laying the marked angles next to each other. 4) Make a conjecture about the sum of the angle measures of the triangle. ...
Pacing
... equations A.A.11 Solve a system of one linear and one quadratic equation in two variables, where only factoring is required. Note: The quadratic equation should represent a parabola and the solution(s) should be integers A.A.12 Multiply and divide monomial expressions with a common base using the pr ...
... equations A.A.11 Solve a system of one linear and one quadratic equation in two variables, where only factoring is required. Note: The quadratic equation should represent a parabola and the solution(s) should be integers A.A.12 Multiply and divide monomial expressions with a common base using the pr ...
File
... congruent. • Show that both pairs of opposite angles are congruent. • Show that one angle is supplementary to both consecutive angles. • Show that the diagonals bisect each other. • Show that one pair of opposite sides are congruent and parallel. ...
... congruent. • Show that both pairs of opposite angles are congruent. • Show that one angle is supplementary to both consecutive angles. • Show that the diagonals bisect each other. • Show that one pair of opposite sides are congruent and parallel. ...
(MFM1P) Unit 2
... As you drag vertices, look for some of the following: • measurements that always seem to be equal to each other • measurements that never seem to change • measurements that might have a constant ratio (proportional) • lines that always seem to be parallel or perpendicular • line segments that always ...
... As you drag vertices, look for some of the following: • measurements that always seem to be equal to each other • measurements that never seem to change • measurements that might have a constant ratio (proportional) • lines that always seem to be parallel or perpendicular • line segments that always ...
More on Neutral Geometry I (Including Section 3.3) ( "NIB" means
... ∠ TAB ≅ ∠ FDE and AB ≅ DE . Therefore, ∆ ABT ≅ ∆ DEF by SAS , and ∴ ∠ ABT ≅ ∠ DEF by CPCF and ∴ m( ∠ ABT ) = m( ∠ DEF ) , which contradicts that fact that m( ∠ ABT ) < m( ∠ DEF ) . ∴ AC ≅ DF . ∴ ∆ ABC ≅ ∆ DEF by SAS . ∴ The ASA Triangle Congruence Condition is valid. Q E D ...
... ∠ TAB ≅ ∠ FDE and AB ≅ DE . Therefore, ∆ ABT ≅ ∆ DEF by SAS , and ∴ ∠ ABT ≅ ∠ DEF by CPCF and ∴ m( ∠ ABT ) = m( ∠ DEF ) , which contradicts that fact that m( ∠ ABT ) < m( ∠ DEF ) . ∴ AC ≅ DF . ∴ ∆ ABC ≅ ∆ DEF by SAS . ∴ The ASA Triangle Congruence Condition is valid. Q E D ...
Mth 97 Winter 2013 Section 6.5 and 7.1 Section 6.5 – Using Laws of
... An ___________ of a circle consists of the points A and B of the circle together with the portion of the circle contained between the two points. Points A and B are called the __________________ of the arc. A __________________________ is an arc whose endpoints are the endpoints of a diameter and is ...
... An ___________ of a circle consists of the points A and B of the circle together with the portion of the circle contained between the two points. Points A and B are called the __________________ of the arc. A __________________________ is an arc whose endpoints are the endpoints of a diameter and is ...
Euler angles
The Euler angles are three angles introduced by Leonhard Euler to describe the orientation of a rigid body. To describe such an orientation in 3-dimensional Euclidean space three parameters are required. They can be given in several ways, Euler angles being one of them; see charts on SO(3) for others. Euler angles are also used to describe the orientation of a frame of reference (typically, a coordinate system or basis) relative to another. They are typically denoted as α, β, γ, or φ, θ, ψ.Euler angles represent a sequence of three elemental rotations, i.e. rotations about the axes of a coordinate system. For instance, a first rotation about z by an angle α, a second rotation about x by an angle β, and a last rotation again about z, by an angle γ. These rotations start from a known standard orientation. In physics, this standard initial orientation is typically represented by a motionless (fixed, global, or world) coordinate system; in linear algebra, by a standard basis.Any orientation can be achieved by composing three elemental rotations. The elemental rotations can either occur about the axes of the fixed coordinate system (extrinsic rotations) or about the axes of a rotating coordinate system, which is initially aligned with the fixed one, and modifies its orientation after each elemental rotation (intrinsic rotations). The rotating coordinate system may be imagined to be rigidly attached to a rigid body. In this case, it is sometimes called a local coordinate system. Without considering the possibility of using two different conventions for the definition of the rotation axes (intrinsic or extrinsic), there exist twelve possible sequences of rotation axes, divided in two groups: Proper Euler angles (z-x-z, x-y-x, y-z-y, z-y-z, x-z-x, y-x-y) Tait–Bryan angles (x-y-z, y-z-x, z-x-y, x-z-y, z-y-x, y-x-z). Tait–Bryan angles are also called Cardan angles; nautical angles; heading, elevation, and bank; or yaw, pitch, and roll. Sometimes, both kinds of sequences are called ""Euler angles"". In that case, the sequences of the first group are called proper or classic Euler angles.