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Topic 1 TRIANGLE

Topic: Triangles

Time: 2 Hours

Answer all the questions.

Short Answer questions

 

  1. Prove that the line joining the midpoints of two of the sides of a triangle is parallel to the other side and half of it.

  2. C

    D

    The diagonals of a quadrilateral ABCD intersect at a point O such that. Prove that ABCD is trapezium.
  1. In the fig if AB || DC|| EF. Prove that.

    F

    E

    If PE||RS, prove that D POE ~ DROS

S

EQQQQQ

Q

P

B

A

 

 

R

  

  

 

  1. A girl of height 120cm is walking past a lamp post at a speed of 1.5 meters per second finds the length of the shadow after 5 seconds to be 125cm. Find the height of the lamp post.
  2. S and T are points on sides PR and QR of DPQR such that ÐP = Ð RTS. Prove that D RPQ ~ DRTS.
  3. If DABC ~ DDEF and their areas are 196 cm2 and 225cm2 respectively. If FD = 22.5cm find CA

  4. P

    S

    If the areas of two similar triangles are equal, prove that the triangles are congruent.

  1. O

    A

    B

    Find  ÐABP and ÐBAQ in the figure if

     ÐOPS = 35° and ÐSOB = 125°

 

 

 

  1. A ladder is placed against a wall such that its foot is at a distance of 3m from the wall to reach a height of 4m. Find the length of the ladder.

 

 

Big Questions

  1. State and prove Basic Proportionality theorem.
  2. Prove that the ratio between the medians, angle bisectors and altitudes are equal in two similar triangles.
  3. A triangle ABC is divided in two parts by drawing a line PQ parallel to the base BC. Find the ratio between AP and PB if the ratio between the area of triangles APQ and Trapezium PQCB is 1:2.
  4. D is the point on the side BC of a triangle ANC such that ÐADC = ÐBAC. Prove that CA2 = CB. CD.
  5. If the angle A of triangle ABC is bisected by AD prove that AB:AC = BD:DC.
  6. State and prove the Pythagoras theorem.
  7. BL and CM are the medians of a triangle ABC right angles at A. Prove that 4(BL2 + CM2) = 5 BC2.
  8. In an equilateral triangle ABC, D is the point on side BC such that BD= BC. Prove that 9AD2 = 7AB2.In any triangle ABC, AD is the median, AE is the altitude. Prove that AC2 = AD2 +BC. DE + Prove that the three times sum of the squares of the medians of a triangle is equal to four times the sum of the squares of their altitudes.

 

 

 

 

 

 


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