2d geometry

Question: (a) A right angled triangle ABC has its vertices A (4, 0), B (0, 0) and C (0, 2). Plot the points on a graph paper and find the area of the triangle. (b) Plot the following points on a graph paper and name the figure formed: P (5, -3), Q (5, 0), R (2, 0). Find its..

Question: Show that the quadrilateral, formed by joining the mid-points of the consecutive sides of a rectangle is a rhombus. Answer: Given: P, Q, R and S are the mid-points of AB, BC, CD and DA respectively. To prove: PQRS is a rhombus. Proof: Consider D BAC ( In..

Question: In the adjoining figure PQR is an equilateral triangle. N is any point on PQ. Show that (i) NR>PN (ii) NR>NQ. Answer: Given: In D PQR, PQ=PR=QR To prove: (i) NR>PN (ii) NR>NQ Proof: In D PQR, PQ=PR=QR ( given) ( Equilateral triang..

Question: In the adjoining figure, LM is the base of isosceles D KLM. Prove that KM>XL. Answer: Given: In D KLM , KL=KM To prove: KM > XL Proof: KL > XL (theorem on inequality KLM is an isosceles triangle) But KL = KM \ KM > X..

Question: P is the mid-point of side BC of a D ABC. If Q is the mid-point of AP and BQ when produced meets AC in L, then prove that [3 Mark] Answer: Given: In triangle D ABC, BP = PC and AQ = QP. To prove: Construction: Through P, draw PM parallel to ..

Question: In figure, D, E and F are respectively, the mid-points of sides BC, CA and AB of an equilater at triangle ABC. Prove that D DEF is also an equilateral triangle. Answer: Given: D, E and F are mid-points of BC, CA and AB respectively. Dh..

Question: Show that a median of a triangle divides it into two triangles of equal area. Answer: Given: In D ABC, AD is one of the medians of D ABC. To prove: Construction: Draw AE ^ BC. Proof: Since BD = DC and h is the same for both the triangl..

Question: Answer: Data: AB = BC and AD = CE To prove: AD = CE Proof: AB=BC (data) AD=CE (data) BD=BE (If equals are subtracted from equals, the remainders are also equal) In D AEB and D CDB, AB=BC (data) BE=BD (proved above) (common angle to both th..

Question: ABC and ABD are two triangles such that AD=BC, BD=AC. Answer: Data: In triangles ABC and ABD, AD=BC and BD=AC. To prove: Proof: Comparing D ABC and D ABD , BC = AD (data) AC = BD (data) AB = AB (common side to both triangles) ..

(supplements of equal angles are equal) In D ABF and D DGE, BF = DG (prove above) AF = GE (data) \ AB = DE (corresponding side..