Proofs with Congruent Triangles Worksheets
How to Prepare Proofs with Congruent Triangles - Triangles that are identical to each other are typically termed as the congruent triangles. These triangles have three sides, and three angles and one or more measurements of these triangles coincide with each other. Knowing how to write proofs for congruent triangles is essential in geometry. These concepts help solve mathematical and geometrical problems. There are some properties that can be crucially helpful in writing and preparing proofs for congruent triangles. The reflexive property of congruence states that any shape is congruent to itself. However, this may seem apparent. But for geometric proofs, you need any aspect that can help solve the problem. Even if two triangles share a common line segment, you can use it as a reflexive property to prove the congruence of the triangle. The symmetric property states that congruence works backward ad frontwards. That means that if an angle ABC is congruent to angle DEF, then the statement stands true other way around too. To express it mathematically, ∠ABC is congruent to ∠DEF then ∠DEF is congruent to ∠ABC. The transitive property of the congruence, if two figures are congruent to a third figure, then they are also congruent to each other. To express it mathematically, we can write: Triangle ABC is congruent to Triangle JLM, and Triangle JLM is congruent to Triangle WYZ, the Triangle ABC is congruent to Triangle WYZ.