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Your teacher will give you a set of cards that show different figures. Sort the cards into categories of your choosing. Be prepared to explain the meaning of your categories.
Sort the cards by rigid vs. flexible figures.
State at least one set of triangles that can be proved congruent using the:
Side-Angle-Side Triangle Congruence Theorem.
Angle-Side-Angle Triangle Congruence Theorem.
Side-Side-Side Triangle Congruence Theorem.
To prove that segments or angles are congruent, we can look for triangles that those segments or angles are part of. Can the triangles be proven congruent? Are the segments or angles corresponding parts of congruent triangles? Does that help prove the conjecture?
To prove that the triangles are congruent, we can look at the diagram and given information. Think about whether it will be easier to find pairs of corresponding angles that are congruent or pairs of corresponding sides that are congruent. Then check if there’s enough information to use the Side-Side-Side, Angle-Side-Angle, or Side-Angle-Side Triangle Congruence Theorem.
Here's an example: As part of a proof to show that a quadrilateral with four congruent sides has parallel opposite sides, we need to show that a diagonal splits the quadrilateral into two congruent triangles.
First, sketch a diagram to see what is given, and look for congruent triangles. Since this is about a quadrilateral, adding a diagonal auxiliary line to make triangles will be helpful.
Because all the sides of the quadrilateral are congruent, and the triangles formed by the diagonals share a third side, we can use the Side-Side-Side Triangle Congruence Theorem to prove that triangles and are congruent.