Proofs with congruent triangles
Japanese school year: Junior high 2
What you learn
Learn how to construct deductive proofs for geometric properties and congruent segments or angles using triangle congruence conditions. Proofs are written step by step based on properties of vertical angles and alternate interior angles. This topic fosters logical reasoning skills and serves as a foundation for geometric exploration.
Key points
These conditions prove that two triangles are congruent. Triangles are congruent if all 3 pairs of sides, 2 pairs of sides and their included angle, or 1 pair of sides and its 2 adjacent angles are equal.
These conditions prove the congruence of right triangles. Two right triangles are congruent if their hypotenuses are equal and either another pair of legs or an acute angle is equal.
This guides how to write a congruence proof. First state matching sides and angles with reasons (such as vertical angles, alternate angles, or common sides), then state the satisfying condition.
Choose a set to practice.