In geometry, congruence means the figures have the same measure and shape. For a student to effectively discuss congruence they must first recognize the figure and its attributes. To achieve this, the learner must be able to differentiate one figure from another. To compare figures and establish that one is congruent to the other or not, the student pulls on an understanding of shapes. To prove congruence, the student makes connections with axioms, properties, analysis, and logic. The study of congruence progresses through the five Van Hiele levels, from recognition of shape to using axiomatic systems within systems. By working with the concept of congruence, the teacher can develop higher-level thinking in the students. With Van Hiele,
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They develop generalizations about their properties. In the first grade, TEK 1(6)(D & E), they begin using formal geometric language while they discuss the attributes. The students begin joining shapes together to form a larger specified shape, TEK (1)(6)(F), which is very important in the ability to eventually prove congruence. They are beginning to see one figure composed of others. They will use this skill later when analyzing proofs. In the second grade, analysis continues as students create shapes with a specified number of sides and vertices. The terms, sides and vertices, are introduced and regular polygons are classified by sides and vertices, TEK 2(8)(A) and TEK 2(8)(C). In the third grade, when the students classify shapes into subgroups TEKS 3(6)(A) and (B), they demonstrate a higher level of thinking. Students can easily see that all four-sided figures are not the same, or congruent, although the term may not have been introduced. In the fourth grade, the TEKS introduce points, lines, line segments, rays and angles, and perpendicular and parallel lines, TEK 4(6)(A). The students apply their knowledge of right angles and identify acute and obtuse triangles, TEK 4(6)(C). They also measure angles, TEK 4(7)(A), and determine the measure of an angle formed by two non-overlapping angles, given one or both angle measures, TEK 4(7)(E ) . They are beginning to see the …show more content…
They examine the Pythagorean theorem, TEKS 8(6)(C), 8(7)(C), and 8(7)(D). Also, in the eighth grade, 63% of the students were successful in identifying properties of orientation and congruence of rotation of objects, TEK 8(10)(A), but only 28% could differentiate between transformations that preserve congruence and those that do not, TEK 8(10)(B). At this stage, they have a good understanding of what congruence is. They are well prepared for geometry in tenth grade, where they will prove congruence of triangles, TEKS G(5)(B), G(6)(B),
They develop generalizations about their properties. In the first grade, TEK 1(6)(D & E), they begin using formal geometric language while they discuss the attributes. The students begin joining shapes together to form a larger specified shape, TEK (1)(6)(F), which is very important in the ability to eventually prove congruence. They are beginning to see one figure composed of others. They will use this skill later when analyzing proofs. In the second grade, analysis continues as students create shapes with a specified number of sides and vertices. The terms, sides and vertices, are introduced and regular polygons are classified by sides and vertices, TEK 2(8)(A) and TEK 2(8)(C). In the third grade, when the students classify shapes into subgroups TEKS 3(6)(A) and (B), they demonstrate a higher level of thinking. Students can easily see that all four-sided figures are not the same, or congruent, although the term may not have been introduced. In the fourth grade, the TEKS introduce points, lines, line segments, rays and angles, and perpendicular and parallel lines, TEK 4(6)(A). The students apply their knowledge of right angles and identify acute and obtuse triangles, TEK 4(6)(C). They also measure angles, TEK 4(7)(A), and determine the measure of an angle formed by two non-overlapping angles, given one or both angle measures, TEK 4(7)(E ) . They are beginning to see the …show more content…
They examine the Pythagorean theorem, TEKS 8(6)(C), 8(7)(C), and 8(7)(D). Also, in the eighth grade, 63% of the students were successful in identifying properties of orientation and congruence of rotation of objects, TEK 8(10)(A), but only 28% could differentiate between transformations that preserve congruence and those that do not, TEK 8(10)(B). At this stage, they have a good understanding of what congruence is. They are well prepared for geometry in tenth grade, where they will prove congruence of triangles, TEKS G(5)(B), G(6)(B),