are congruent triangles the same size?
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Definition: Triangles are congruent when all corresponding sides and interior angles are congruent. The triangles will have the same shape and size, but one may be a mirror image of the other.
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Not all lines that divide a figure into two congruent halves are lines of symmetry. The diagonal of a rectangle divides the rectangle into two triangles that are congruent (same size and shape). But the diagonal line is NOT a line of symmetry. Folding along the diagonal does not coincide with the other side.
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Whereas, similar polygons have the same shape, but not the same size (i.e., one is bigger than the other). This means that if two polygons are similar, then their corresponding angles are congruent but their their corresponding sides are proportional as displayed in the figure below.
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All circles of the same size are congruent to one another. "Size" can refer to radius, diameter, circumference, area, etc.
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Answer and Explanation: The diagonals of a trapezoid are only congruent (have the same length) if the trapezoid is an isosceles trapezoid.
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If two pairs of corresponding angles in a pair of triangles are congruent, then the triangles are similar. We know this because if two angle pairs are the same, then the third pair must also be equal. When the three angle pairs are all equal, the three pairs of sides must also be in proportion.
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Determining congruence SAS (Side-Angle-Side): If two pairs of sides of two triangles are equal in length, and the included angles are equal in measurement, then the triangles are congruent.
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Congruent Angles have the same angle (in degrees or radians). That is all. These angles are congruent. They don't have to point in the same direction. They don't have to be on similar sized lines.
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All equilateral triangles have the same same shape (three equal sides, three equal angles). All equilateral triangles are similar. A hexagon only needs to have six sides. ... All hexagons are not similar.
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The right triangles trs and wuv are congruent when they have equal lengths of the sides and having equal sides, angles should as well be equal with the two triangles.
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Congruence is a relationship of shapes and sizes, such as segments, triangles, and geometrical figures, while equality is a relationship of sizes, such as lengths, widths, and heights. Congruence deals with objects while equality deals with numbers. You don't say that two shapes are equal or two numbers are congruent.
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1. As an isosceles triangles, the length of 2 sides of any special 45 45 90 triangle will always be the same. ... As a consequence of having equal lengths, a corresponding property of these two sides is that they have angles of the same size. This can be identified by the two 4 5 45 45° angles in the diagram above.
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2 Answers By Expert Tutors All equilateral triangles have the same same shape (three equal sides, three equal angles). ... A hexagon only needs to have six sides. Not all hexagons are the same shape. All hexagons are not similar.
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The bases (top and bottom) of an isosceles trapezoid are parallel. Opposite sides of an isosceles trapezoid are the same length (congruent). The angles on either side of the bases are the same size/measure (congruent).
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Figures are similar if they have the same shape - the size may be different. All equilateral triangles have the same same shape (three equal sides, three equal angles). ... Not all hexagons are the same shape. All hexagons are not similar.
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The diagonal of a rectangle divides the rectangle into two triangles that are congruent (same size and shape). But the diagonal line is NOT a line of symmetry. ... In regular polygons (where all sides are congruent and all angles are congruent), the number of lines of symmetry equals the number of sides.
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Not all lines that divide a figure into two congruent halves are lines of symmetry. The diagonal of a rectangle divides the rectangle into two triangles that are congruent (same size and shape). But the diagonal line is NOT a line of symmetry. ... The parallelogram, however, has NO lines of symmetry.