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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.

State the condition of congruency.

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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.

(i). $\u25b3ABD\cong \u25b3ACD$

(ii). AD is bisector $\angle A$.

(iii). AD is perpendicular to BC.

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.

Q. Prove that $\u2206$

ABCis right-angled atAifAB= 2n+ 1,AC= 2n(n+ 1) andBC= 2n(n+ 1) + 1.^{∘}. AD = AB = 6 CM, BC = 3.6 CM, CD = 5 CM. Measure < BCD.Q.(b) In figure (ii) given below, ABCD is a quadrilateral in which AB = AD, $\angle A=90\xb0=\angle C$, BC = 8 cm and CD = 6 cm. Find AB and calculate the area of $\u25b3$ABD.

(i)

(ii)

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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$\xb0$, y$\xb0$ and z$\xb0$ in ascending order of their values.

Q.37. In the adjoining figure, AB || DC. CE and DE bisects $\angle BCDand\angle ADC$ 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 AC$\perp $CB, 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.