Areas Of Two Similar Triangles Theorem 1: The ratio of the areas of two similar triangles are equal to the ratio of the squares of any two corresponding sides. Given: Two triangles ABC and DEF such that ∆ABC ~ ∆DEF. To Prove: Construction: Draw AL ⊥ BC and DM ⊥ EF. Proof: Since similar triangles are equiangular and their corresponding sides are proportional. … [Read more...] about Areas Of Two Similar Triangles
Triangles
Criteria For Similarity Of Triangles
Criteria For Similarity Of Triangles AAA similarity criterion: If in two triangles, corresponding angles are equal, then the triangles are similar. AA Similarity criterion: If in two triangles, two angles of one triangle are respectively equal the two angles of the other triangle, then the two triangles are similar. SSS Similarity criterion: If in two triangles, … [Read more...] about Criteria For Similarity Of Triangles
How to Prove the Angle Sum Property of a Triangle
Angle Sum Property of a Triangle Theorem 1: Prove that sum of all three angles is 180° or 2 right angles. Given: ∆ABC To prove: ∠A + ∠B + ∠C = 180° Construction: Draw PQ || BC, passes through point A.Proof: ∠1 = ∠B and ∠3 = ∠C ....... (i) [∵ alternate angles ∵ PQ || BC] ∵ PAQ is a line ∴∠1 + ∠2 + ∠3 = 180° (linear pair application) ∠B + ∠2 + ∠C = … [Read more...] about How to Prove the Angle Sum Property of a Triangle
Theorems and Postulates for Geometry
Theorems and Postulates for Geometry This is a partial listing of the more popular theorems, postulates and properties needed when working with Euclidean proofs. You need to have a thorough understanding of these items. General:Reflexive Property A quantity is congruent (equal) to itself. a = aSymmetric Property If a = b, then b = a.Transitive … [Read more...] about Theorems and Postulates for Geometry