Congruent Shapes
Congruent Shapes
Understanding Congruency in Geometric Shapes
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Define congruent shapes as shapes that are identical in form, having the same size and shape.
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Understand that if two shapes are congruent, they can be transformed into one another through rotations, translations, and reflections only.
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Comprehend that reflections, translations, and rotations are known as isometries as they do not change the size and shape of a figure.
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Appreciate that all sides and angles of a congruent shape should match exactly when superimposed on the original shape.
Criteria for Congruency
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Understand four main congruency rules: Side-Side-Side (SSS), Side-Angle-Side (SAS), Angle-Side-Angle (ASA), and Right Angle-Hypotenuse-Side (RHS).
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Recall the Side-Side-Side (SSS) rule: If all three sides of one triangle are equal to the corresponding sides of another triangle, the triangle are congruent.
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Understand the Side-Angle-Side (SAS) rule: If two sides and the included angle in one triangle are equal to corresponding two sides and included angle in another triangle, the triangles are congruent.
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Comprehend the Angle-Side-Angle (ASA) rule: If two angles and the included side in one triangle are equal to the corresponding angles and side in another triangle, the triangles are congruent.
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Recall the Right Angle-Hypotenuse-Side (RHS) rule: If in two right-angled triangles, the hypotenuse and one side of one triangle are equal to the hypotenuse and one side of the other triangle, the triangles are congruent.
Applying Congruency Concepts
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Recognize that congruent shapes have equal areas.
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Understand that congruent shapes have equal perimeters.
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Apply congruency rules to prove congruency in various geometric shapes and figures.
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Use congruent shapes to solve geometric problems and real-life application problems.
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Solve problems involving congruency in triangles and other polygons.
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Acknowledge that non-identical shapes can still be congruent, and different orientations of a shape can be congruent to each other. Remember that being congruent doesn’t mean having the same orientation or being in the same position.