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Syllabus
Q.74. In the parallelogram ABCD, M is mid-point of AC and X, Y are points on AB and DC respectively such that AX = CY.
Prove that :
(i) triangle AXM is congruent to triangle CYM,
(ii) KMY is a straight line.
1. the actual length of the diagonal distance AC of the plot in km.
2. the actual area of the plot in sq km.
(i) the actual length of the diagonal distance AC of the plot in km.
(ii) the actual area of the plot sq km.
11. (a) In the quadrilateral (1) given below, AD = BC. P, Q, R and S are mid-points of AB, BD, CD and AC respectively. Prove that PQRS is a rhombus.
(b) In the figure (2) given below, ABCD is a kite in which BC = CD, AB = AD. E, F, G are mid-points of CD, BC and AB respectively. Prove that
(i) = 90°.
(ii) the line drawn through G and parallel to FE bisects DA.
Graphics
If AO = 2CO and BO = 2DO; show that:
(i) ∆AOB is similar to ∆COD.
(ii) OA × OD = OB × OC.
1) M , N and A are collinear.
2) A is the mid point of MN.
Please do not provide any link.
Q. In triangle PQR, MN||QR and
(i) Find
(ii) Prove that triangle OMN and ORQ are similar
(iiI) Find, area of triangle OMN : area of triangle ORQ
Prove that
I) angle PQR = 90 DEGREE
II) Line through P and parallel to QR bisects side AD
2. A train travelling at 40 km/h takes 3 hours for a journey. How long will it take the train to complete the same journey, travelling at 90 km/h?
A. 2 hours
B. 1 hour
C. 4 hours
D. 1 hour 20 min
(b) In PQR, MN is parallel to QR and
(i) Find
(ii) Prove that OMN and
ORQ are similar.
(iii) Find , Area of OMN : Area of ORQ
1)PM^2 + RN^2 = 5MN^2
2)4PM? = 4PQ? + QR?
3)4RN? = PQ? + 4 QR?
4)4 (PM? + RN ?)=5 PR?
1) AC is greater than AD
2) AE is greater than AC
3) AE is greater than AD
(i) the length of PQ, if BC=7.5cm.
(ii)the area of triangle APQ: area of triangle ABC
(iii)the area of triangleAPQ:area of PBCQ