How Do You Prove Triangles Are Congruenthttps://www.youtube.com/watch?v=GmS-p1S_t5ECongruent FiguresTwo figures/objects are said to be congruent if they are exactly of the same shape and size. The relationship between two congruent figures is called con…

Pythagoras TheoremTheorem 1: In a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Given: A right-angled triangle ABC in which B = ∠90º. To Prove: (Hypotenuse)2 = (Base)2 + (Perpendicular)2. …

How Do You Find The Angle Of An Isosceles Triangle Theorem: Angles opposite to equal sides of an isosceles triangle are equal. Given: In ∆ABC, AB = AC To Prove: ∠B = ∠C Construction: Draw AD, bisector of ∠A ∴ ∠1 = ∠2 Proof: In ∆ADB & ∆ADC AD = AD   …

Criteria For Congruent Triangleshttps://www.youtube.com/watch?v=QkU4FZN8MY0Congruent triangles are triangles that have the same size and shape. This means that the corresponding sides are equal and the corresponding angles are equal. Congruent Triangles …

Classification of TrianglesA triangle is a polygon with three sides. It has three sides and three vertices. There are seven types of triangles. The sum of the angles of a triangle is 180°.Triangles Types can be classified in two ways: By their sidesBy t…

Areas Of Two Similar TrianglesTheorem 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:  \(\frac{Area\ (\Delta ABC)}…

Criteria For Similarity Of TrianglesAAA 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 an…

Angle Sum Property of a TriangleTheorem 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) [∵ alt…

Theorems and Postulates for GeometryThis 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 PropertyA quantit…