CBSE:10th Math :Chapter Triangles : Solved Concept builder theorems




If a line divides any two sides of a triangles proportionally then the line is parallel to the third side
Statement: If a line divides any two sides of a triangles proportionally (in same ratio), then the line is parallel to the third side.

Proof: We are given ABC 
AD / BD = AE / CE

We have to prove: DE is parallel to BC

Let DE's not parallel to BC then an another line DE' is parallel to BC.

Now

AD / BD = AE / CE [Given]

And AD / BD = AE' / CE' [Thales Theorem]

Therefore AE / CE = AE' / CE'

i.e. AE / CE + 1 = AE' / CE' + 1

i.e. AE + CE / CE = AE' + CE' / CE' 

i.e. CE = CE'

But this is not possible until E and E' is coincident.

Thus, our assumption is wrong and DE is parallel to BC.
X Triangles :Criteria for Similarity of Triangles Solved: 

Comments

  1. J.Sunil SirJune 11, 2012 at 8:13 AM

    X Similar Triangle test paper-1
    Download File
    X Similar Triangle test paper-2
    Download File
    http://jsuniltutorial.weebly.com/x-similar-triangles.html

    ReplyDelete

Post a Comment

Popular Post

Obtaining and Utilization Food Class 7 Science Solved question (Basic Science Questions answers)

Image
A. Answer these questions 1. Name the three life process help living being to procure energy from food? Answer: Three life processes that help living organisms to procure energy from food are: (i) Digestion (Nutrition) (ii) Respiration (iii) Transportation 2. What are Autotrophs? Name an organism other than other than green plant that is an autotroph. Answer: Autotrophs are organisms that can prepare their own food. Chlamydomonas is a type of green algae which is an example of an autotroph, other than green plants. Cyanobacteria are also an example of autotroph. 3. Name three type of heterotrophic nutrition Answer: Three types of heterotrophic nutrition are: (i) Saprophytic nutrition (ii) Parasitic nutrition (iii) Holozoic nutrition 4. What are enzymes? Answer: Enzymes are chemical substances that act as biological catalysts and are important for carrying out biochemical processes, such as digestion, in our body
Read more

Plants fiber and fabric solution Cordova Learning Science class07

Image
A Tick the correct options: 1. Which of the following is not a natural fibre? (a) cotton (b) rayon √ (c) silk (d) wool 2. Lohi is the breed of (a) cow (b) silk moth (c) sheep √ (d) buffalo 4. Sheep are sheared in season (a) summer √ (b) spring (c) autumn Ö (d) winter 3. How many weeks are required for the eggs of silk moth to hatch? See book (a) one (b) two √ (c) three (d) four 6. Which of the following silk is produced when raw silk is twisted? (a) spun (b) coloured (c) thrown √ (d) mooga 5. What do we call the silky covering spun by the silkworm for its protection? (a) moth (b) larvae (c) pupa (d) cocoon√ B. Fill in the blanks: 1. Alpaca is generally f
Read more

10 class acids salt and base Exam oriented Board Questions

Image
Q. How is NH4OH used as a laboratory reagent? Answer:  NH4OH is used to detect cations in their salt solutions by precipitating their hydroxides whose colour and solubility in excess NH4OH, identifies them. Q. Though NaHSO 4  solution releases H +  ions, why is it not called an acid? Answer:  NaHSO 4  solution is not called an acid because an acid should release only H +  ions as positive ions and not any other positive ions. But NaHSO 4  is solution releases H +  ions as well as Na +  ions also as positive ion. Q. How would you distinguish between baking powder and washing soda by heating? Answer: Sodium hydrogencarbonate on heating gives CO2 gas which will turn lime water milky whereas no such gas is obtained from sodium carbonate. 2NaHCO3 ---Heat → Na2CO3 + H2O + CO2      Na2CO3.10H2O -Heat → Na2CO3 + 10H2O Q. Why aqueous solution of sodium carbonate is basic in nature? Answer: Sodium bicarbonate is an amphoteric compound. Aqueous solutions are mildly alkaline due
Read more

HEREDITY AND EVOLUTION SOLVED EXERCISES QUESTIONS [Biology Term-2 CHAPTER - 13]

Q.1. What is heredity? Ans:- Heredity refers to the transmission of characters or traits from the parents to their offspring. Q.2. Name the plant on which Mendel performed his experiments? Ans:- Garden Pea ( Pisum sativum .) Q.3. Define variation? Ans:-Variation refers to the differences in the characters or traits about the individuals of a species. Q.4. Define a gene? Ans:- Gene is a small segment of DNA on a chromosome occupying specific position in which is a hereditary determinant or unit of a biological function. Q.5.Write the expanded form of DNA? Ans:- DNA - Deoxyribonucleic Acid. Q.6. What are the components of chromosome? Ans:- Each chromosome is double or replicated and consists of two thread like structures called chromatids attached to each other at centromere. .Each chromatid has a number of dense areas arranged linearly which are known as chromomeres. They represent the areas of active genes. .Internally each chromosome has two spirally coiled
Read more

Magnetic Effects of Electric Current - CBSE Board Test Questions for class 10

Image
Central Public School,Samastipur and Sadhana Devi Vidyapith Assignment SA-1 Chapter: Magnetic Effects of Electric Current Section-A [1marks] 1. What does the direction of thumb indicate in the right-hand thumb rule? 2. What is the frequency of alternating current in India? 3. How will you use a solenoid to magnetize a steel bar? 4. An alternating electric current has a frequency of 50 Hz. How many times does it change its direction in one second? 5. Name devices which produce: (i) alternating current, (ii) direct current. 6. Name the physicist who discovered the magnetic effect of the electric current. 7. A straight copper conductor is held parallel to the axis of a freely suspended magnetic needle such that the conductor is under the needle and the current is flowing from south to north. In which direction the north of magnetic needle will move? 8. If a copper conductor carrying a current is held in north-south direction, in which direction will its magnetic fiel
Read more