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| 11.1 Concepts It is common knowledge from high school geometry and from reading section 11.1 that two triangles are congruent if they satisfy the SSS, ASA, or SAS property. In general, there is no SSA property for congruence of triangles. Evaluate the following conjecture by drawing several diagrams to help you make a case for supporting the statement (SSA property) or finding a counter example. Conjecture: If in a triangle, an obtuse angle, the side opposite the obtuse angle, and one other side are congruent to an obtuse angle, the side opposite the obtuse angle, and one other side of another triangle, the two triangles are congruent. 11.1 Teaching With well-designed activities, appropriate tools, and teacher's support, students can make and explore conjectures about geometry and can learn to reason carefully about geometric ideas from the earliest years of schooling. NCTM Standards 2000, page 40If a line is drawn on paper, small markers such as beans, centimeter cubes, etc., can be placed on the paper and easily moved about to represent the points on another line which, for example, is perpendicular or parallel to the original. Using such markers to represent points, write a brief lesson with a series of activities and questions to involve students in learning about an angle bisector and the perpendicular bisector of a segment. 11.1 Concepts If four sides of one quadrilateral are congruent to four sides of another quadrilateral, are the two quadrilaterals congruent? Formulate two congruence properties for quadrilaterals that are similar to the SSS, SAS, and ASA properties for triangles. Use diagrams to illustrate your conclusions. |