Geometry 8 Mark Creative Question Paper With Answer Key

10th Standard

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Maths

Time : 01:00:00 Hrs
Total Marks : 96

    8 Marks

    12 x 8 = 96
  1. In the figure, if \(\triangle A B E \cong \triangle \text { ACD, show that }\triangle A D E \sim \triangle A B C\)

  2. Prove that the area of an equilateral triangle described on one side of a square in equal to half  the area of the equilateral triangle described on one of its diagonals.

  3. Construct an isosceles triangle whose base is 8 cm and altitude 4 cm and then another triangle whose sides are \(1 \frac{1}{2}\) times the corresponding sides of the isosceles triangle.

  4. O is any point inside a triangle \(\Delta\)ABC The bisector of \(\angle A O B, \angle B O C, \angle C O A\) meet the sides AB, BC and CA in point D, E and F respectively. Show that AD x BE x CF = DB x EC x FA.

  5. In AD is the median of  \(\Delta\)ABC The bisector of \(\angle\)ADB and \(\angle\)ADC meet AB and AC in E and F respefiively. Prove that EF || BC

  6. The bisectors of the angle B and C of a triangle ABC, meet the opposite sides in D and E respectively. If DE DE || BC BC, prove that the triangle is isosceles

  7. P and Q are points on the sides CA and CB respectively of \(\Delta\)ABC right angled at C. Prove that AC2 + BP2 = AB2 + PQ2.

  8. ABC is a right triangle right angled ar C and \(\mathrm{AC}=\sqrt{3} \mathrm{BC} \text {. Prove that } \angle A B C=60^{\circ} \text {. }\)

  9. A point O tn the lnterior of a rectangle ABCD is joined with each of the vertices A, B, C and D.Prove that OB2 + OD2 = OC2 + OA2

  10. Show that the alternates of a triangle are conctrrent.

  11. Draw a circle of radius 5 cm. Consider a point P at a distarce of 8 cm from the circle's centre and draw two tangents from P.

  12. Construct a \(\triangle\) PQR in which PQ = 8 cmR = 60o and the median RG from R to PQ is 5.8 cm. Find the length of the altitude from R to PQ.

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