Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.
Las rectas y son paralelas y . Encuentra los ángulos , , , , , y .
Parallel lines l and m, intersected by a diagonal line running down and to the left. Angles A through H are marked. On the left side of the diagonal, starting above line l and moving downward, angles are marked as follows: B, C, F, G. On the right side of the diagonal, starting above line L and moving downward, angles are marked as follows: A equals 42 degrees, D, E, H. Circles are drawn around angles A, B C and D and angles E, F, G and H.
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1.2
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Si sabemos esto, entonces sabemos aquello
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1.3
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Hagamos cuadriláteros
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Student Lesson Summary
Si una parte de una figura original es llevada a una parte de la imagen, decimos que esas dos partes son partes correspondientes. La parte puede ser un ángulo, un punto o un lado. Podemos hallar ángulos correspondientes, puntos correspondientes o lados correspondientes.
Si dos figuras son congruentes, entonces hay una transformación rígida que lleva una figura a la otra. Esa misma transformación rígida se puede aplicar a solo una parte de la figura (por ejemplo, un segmento o un ángulo) porque las transformaciones rígidas se aplican a todos los puntos del plano. Por esta razón, las partes correspondientes de dos figuras congruentes también serán congruentes.
Con una traslación y una rotación, podemos llevar el cuadrilátero al cuadrilátero . Ahora que sabemos que las dos figuras son congruentes, también sabemos que todas sus partes correspondientes son congruentes. Todas estas afirmaciones (¡y muchas más!) son verdaderas:
El ángulo es congruente al ángulo .
El segmento es congruente al segmento .
El ángulo es congruente al ángulo .
El segmento es congruente al segmento .
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Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.
Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.
Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.
Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.