In this lesson, students review triangle congruence criteria and practice writing proofs that use triangle congruence theorems. Students begin by identifying corresponding parts in a pair of congruent triangles and practice naming the theorem that proves the triangles are congruent. Students continue that practice in the following activity with pairs of triangles that aren’t necessarily congruent. Finally, students use triangle congruence theorems to write a proof about two triangles formed by the diagonals of a quadrilateral. The proof can be written using any of the three triangle congruence theorems. Students who complete a proof early will be asked to try the proof using a different congruence theorem, which encourages them to make sense of the problem and persevere in solving it (MP1).
Identify a triangle congruence theorem that proves two triangles are congruent.
Identify corresponding parts in congruent figures.
Use the triangle congruence theorems to prove (in writing) figures congruent.
Let’s identify congruent triangles and corresponding parts.
Prove theorems about parallelograms. 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.
Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to ; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.
Prove theorems about parallelograms. 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.