Once the triangles are congruent, then the corresponding parts are congruent, and so we can conclude that the diagonals are congruent.Īnd so the journey continues … with an apology to my former students for not using scissors more often. How can we show that ∆ACD and ∆BDC are congruent?Ībout the perpendicular bisector of segments AB and CD. What is the image of ∆ACD when we rotate it 180˚ about the intersection of the diagonals? What is the image of ∆ACD when we rotate it 90˚ about the intersection of the diagonals? ![]() After students write their proof that triangle (LMN) is congruent to triangle (PQR), invite them to create a visual display of their proof. Use this routine to help students develop the mathematical language of geometric proofs. (I’m not sure whether they really thought we should rotate by 90˚ or they chose 90˚ because we seem to rotate by 90˚ and 180˚ more than any other angle measure.) Representing, Conversing: MLR7 Compare and Connect. (Opposite sides of a rectangle are congruent, all angles in a rectangle are right and thus congruent, and CD=CD by reflexive.)īut a pair of girls wanted to use a rigid motion to show that the triangles were congruent. One student showed the two triangles congruent by SAS. Which two triangles should we show congruent if we want to show that the diagonals are congruent? Students used look for and make use of structure to compose the rectangle into two triangles. (If you read my last post on the diagonals of an isosceles trapezoid, you’ll know why.) ![]() I had a few students come in during zero block to work on proofs. Liliana tried to prove that M N M P in the following diagram. How can you use rigid motions to show that the diagonals of a rectangle are congruent? 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.
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