Question 33 Prove that if a line is drawn parallel to one side of a triangle intersecting the other two sides in distinct points, then the other two sides are divided in the same ratio.

So, we can write this number as; 7√5 = a b. Here a and b are two co prime numbers and b ≠ 0. ⇒ √5 = a 7b ---- (i) R.H.S of equation (i) is rational number but we know that √5 is irrational number. It is not possible. That means our assumption is wrong. Therefore, 7√5 is an irrational number. Suggest Corrections.

Explanation: Let us assume that √5 is a rational number with p and q as co-prime integers and q ≠ 0 ⇒ √5 = p / q On squaring both sides we get, ⇒ 5q 2 = p 2 ⇒ p 2 is a prime number that divides q. Therefore, p is a prime number that divides q Let p = 5x where x is a whole number By substituting the value of p in 5q 2 = p 2, we get ⇒ 5q 2 = (5x) 2

Prove that the parallelogram circumscribing a circle is a rhombus. Solution STEP 1 : Assumption Consider a parallelogram A B C D which is circumscribing a circle with a centre O. Since A B C D is a parallelogram, A B = C D and B C = A D. STEP 2 : Proving that A B C D is a rhombus

Diagonals AC and BD of a quadrilateral ABCD intersect at O in such a way that ar (AOD) = ar(BOC). Prove that ABCD is a trapezium. Solution It is given that, Area(ΔAOD) =Area(ΔBOC) Area(ΔAOD)+Area(ΔAOB) =Area(ΔBOC)+Area(ΔAOB) [Adding Area (ΔAOB) to both sides] Area(ΔADB) =Area(ΔACB)

This video provides the complete proof of this theorem. Link of book is followhttps://s.docworkspace.com/d/AJBn-_yN_MslyumKwpOnFA

Ask doubt Trigonometric Identities CBSE X Maths Introduction to Trigonometry Prove that : cotA + cosecA - 1/cotA-cosecA+1 = 1+cosA / sinA Asked by 20th September 2012 10:07 PM Answered by Expert CBSE X Maths tanA+secA-1/tanA-secA+1=1+sinA/cosA Asked by Adithya Rao 18th May 2014 8:49 AM Answered by Expert CBSE X Maths Introduction to Trigonometry

2 Tips: At least mention that you use commutativity: (−1)(a) = (a)(−1) ( − 1) ( a) = ( a) ( − 1). Put some words alongside your steps. And you actually use that additive identity is unique in jumping from −a + [−(−a)] = 0 − a + [ − ( − a)] = 0 to −(−a) = a − ( − a) = a. – David P

INTRODUCTION TO TRIGNOMETRY HOTS 1. Prove that 2. If tanA=n tanB and sin A =m sin B, prove that n 2 - 1 3. Prove that following identity, where the angle involved is acute andgle for whhc the expression are expressed using identity cosec 2 A= 1+cot 2 A 4. If x sin 3 |+ y cos 3 |=sin|cos| and xsin|=ycos|, prove x 2 +y 2 =1. 5.

Basic proportionality theorem (or Thales theorem): If a line is drawn parallel to one side of a triangle intersecting the other two sides then the line divides these sides in the same ratio. Step 1: Paste the sheet of white paper on the cardboard. Step 2: Draw a straight line PQ = 10 cm on this paper. At P draw a line MP perpendicular to PQ and.

Best Answer Copy Given:In a triangle ABC in which EF BC To prove that:AE/EB=AF/FC Construction:Draw EX perpendicular AC and FY perpendicular AB Proof:taking the ratios of area of triangle AEF.

Answer: prove of BPT :- Step-by-step explanation: Converse of Basic proportionality Theorem. Statement : If a line divide any two sides of a triangle (\Delta )(Δ) in the same ration, then the line must be parallel (||) to third side.