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Syllabus
17. In the given figure, M is mid-point of AB and DE, whereas N is mid-point of BC and DF.
Show that : EF = AC.
(i).
(ii). AD is bisector .
(iii). AD is perpendicular to BC.
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Q.19. The following figure shows a triangle ABC with exterior angles as x, y and z.
(i) If AB > AC > BC; arrange the angles x, y and z in ascending order of their values.
(ii) In the same figure, if y > x > z; arrange sides AB, BC and AC in descending order of their lengths.
Q. In the given figure AB = AC; angle A = 50 degree and angle ACD = 15 degree. Show that BC = CD.
Q.13. Find the area and the perimeter of a square whose diagonal is 10 cm long.
State the condition of congruency.
Q.37. In the adjoining figure, AB || DC. CE and DE bisects respectively. Prove that AB = AD + BC.
Q.7. For going to a city B from city A, there is route via city C such that ACCB, AC = 2x km and CB = 2 (x + 7) km. It is proposed to construct a 26 km highway which directly connects the two cities A and B. Find how much distance will be saved in reaching city B from city A after the construction of highway.
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Q.17. In the following figure; AB is the largest and BC is the smallest side of triangle.
Write the angles x, y and z in ascending order of their values.
Q.(b) In figure (ii) given below, ABCD is a quadrilateral in which AB = AD, , BC = 8 cm and CD = 6 cm. Find AB and calculate the area of ABD.
(i)
(ii)
Q. Prove that ABC is right-angled at A if AB = 2n + 1, AC = 2n (n+ 1) and BC = 2n (n + 1) + 1.
Answer the 1st question.
Q.1. In the given figure, PAAB; PA = QB. If PQ intersects AB at M, show that M is the mid-point of both AB and PQ.
Q.17. In ABC, AB = AC = x, BC = 10 cm and the area of ABC is 60 . Find x.
Q.36. In the adjoining figure, AB = AC, D is a point in the interior of ABC such that DBC = DCB. Prove that AD bisects BAC of ABC.