triangles

Q) In the given figure, ABCD is a quadrilateral. Diagonal BD bisects ∠ B and ∠ D both. Prove that:(i) Δ ABD ~  Δ CBD(ii) AB = BC Ans: VIDEO SOLUTION STEP BY STEP SOLUTION Given: (i) ABCD is a quadrilateral and (ii) BD is angle bisector of ∠ B and ∠ D. (i) To […]

Q) Diagonals AC and BD of a trapezium ABCD intersect at O, where AB || DC. If DO/OB = 1/2, then show that AB = 2CD Ans: Let’s make a diagram for the given question: In Δ AOB and Δ COD,  ∠ ABO = ∠ CDO (being traversal alternate angles with AB ǁ CD)  similarly ∠

Q) If Δ ABC ~ Δ DEF and AB = 4 cm, DE = 6 cm, EF = 9 cm and FD = 12 cm, find the perimeter of Δ ABC. Ans: Let’s start with the diagram for he given question: Step 1: Since we are given that Δ ABC ~ Δ DEF, ∴ Step 2:

Q) In a Δ ABC, D and E are points on the sides AB and AC respectively such that BD = CE. If ∠B = ∠C, then show that DE ǁ BC Ans: Let’s start with the diagram for he given question: Step 1: We are given ∠ B = ∠ C, ∴ AB = AC 

Q) ABCD is a trapezium with AB ǁ DC. AC and BD intersect at E. If Δ AED ~ Δ BEC, then prove that AD = BC.   Ans: Let’s start with the diagram for he given question: Step 1: We are given AB ǁ DC, hence let’s look at △AEB and △CED:  Here we

Q) In the given figure PA, QB and RC are each perpendicular to AC. If AP = x, BQ = y and CR = z, then prove that 1/x + 1/z = 1/y Ans: Step 1: In Δ APC and Δ BQC, ∠ PCA = ∠  QCB  (common angle) ∠ PAC = ∠  QBC  (900)