CBSE ADDA

CBSE Exam  Congruence of  Triangle Solved Questions Q. 1. Prove that Sum of Two Sides of a triangle is greater than twice the length of median drawn to third side. Given:   Δ ABC in which AD is a median. To prove:   AB + AC > 2AD. Construction:   Produce AD to E, such that AD = DE. Join EC. Proof:   In ΔADB and ΔEDC, AD = DE              (Construction) BD = BD             (D is the mid point of BC) ∠ ADB = ∠ EDC       (Vertically opposite angles) ∴ ΔADB   ≅       ΔEDC   (SAS congruence criterion) ⇒ AB = ED               (CPCT) In ΔAEC, AC + ED > AE           ( Sum of any two sides of a triangles is greater than the third side ) ∴ AC + AB > 2AD      ( AE = AD + DE = AD + AD = 2AD & ED = AB ) Q. 2.  ABC is an isosceles triangle in which AB = AC. Side BA is produced to D such that AD = AB (see the given figure). Show that ∠ BCD is a right angle. In ΔABC, AB = AC

CBSE Class IX Introduction to Euclid's geometry   In geometry, we take a point, a line and a plane as undefined terms. An axiom or a postulate is a mathematical statement which is assumed to be true without proof. These assumptions are actually obvious universal truths. We use the term postulate for the assumptions that were specific to geometry. Axioms, on the other hand are assumptions used throughout mathematics and not specifically linked to geometry. Theorems are statements which are proved, using definitions, axioms, previously proved statements and deductive reasoning. Some of the Euclid’s axioms are : (i) Things which are equal to same thing are equal to one another. (ii) If equals are added to equals, the wholes are equal. (iii) If equals are subtracted from equals, the remainders are equals. (iv) Things which coincide with one another are equal to one another.