### Triangle Part - II ( Advanced)

If two triangles are congruent they have equal sides, equal areas.

Condition for Congruence
SAS Theorem:
If two sides and the angle between these two sides (included angle) of one triangle are congruent to the corresponding two sides and the included angle of a saecond triangle, then the two triangles are congruent

Example:

AAS Theorem:
If two angles and a side not between these two angles of one triangle are congruent to two angles and the corresponding side not between these two angles of a second triangle, then the two triangles are congruent

Example:

Hypotenuse-Leg Theorem:

If the hypotenuse and leg of a right triangle are congruent to the hypotenuse and corresponding leg of a second right triangle, then the two triangles are congruent

Example:

Pythagoras’ Theorem: In a right angle triangle the square of the hypotenuse is equal to the sum of the squares of other two sides.

b2=a2+c2

Pythagorean Triplet: There are certain triplets which satisfy the pythagoras’ theorem and are commonly, called pythagorean triplet.
For example: 3, 4, 5;    5, 12, 13;    24, 10, 26;    24, 7, 25;    15, 8, 17

Appolonious Theorem:

In triangle ABC, AD is median, which divides BC into two equal parts. Then,

Stewart theorem:

In Triangle ABC, AD divides side BC in the ratio m and n. (Here AD need not be median) then,
m.b2+n.c2=a(d2+mn)

Mean proportionality and Mid Point theorem:

In the first triangle, DE // BC so AD / DB = AE / EC
In the second triangle, D and E are mid points of AB and AC respectively. Which implies,
AD / DB = AE / EC = 1
Also, DE = 1 / 2 BC

### Spotting Error Quiz IV - With Explanation For SSC Exam 2015

Hello Readers, As you know that Spotting Error types question is an important part of competitive examinations and seldom any book provide you the detailed solution. So we have decided to provide you the previous year questions of  spotting error along with the Explanation . If you like it let us know, you can also ask for detailed solutions of questions that are bothering you. 1.     I found (a)/ the two first chapters of the book (b)/ particularly interesting. (c)/ No error (d) Answer    (b) Explanation : It should be   ‘the first two chapters’ . 2.     Bacon, the father of the English easy (a) / had a thirst (b) / of knowledge (c) / No error (d) Answer    (a) Explanation : The English means the citizen of England.   Article is not used before language

### English Error Spotting - Previous Year Questions of SSC CGL

Competition Zenith brings you a post on Error Spotting to boost your English for competitive exams. We are providing you the specifically chosen questions from previous year papers of SSC CGL with the best possible explanation in simplest of the language. Below are some questions with explanation: Questions 1. Have trust on(a)/God and everything(b) /will be right.(c) /(d) No error 2. The cattles (a) /are grazing (b) /in the fields.(c) /(d) No error 3. He is one of (a)/ the best novelists (b) /that has ever lived. Do you agree? (c)/no error (d) 4. On a rainy day (a) /I enjoy to watch TV (b) / with a hot cup of tea.(c ) /no error(d) 5. No sooner did (a)/I reach (b)/ Patna railway station than the train departed(c)/no error (d) 6. There is no agreement (a) / between you and I (b) /so we are free to go our way(c) /no error (d) 7. A variety of books (a) / is available in the market (b) / to help the students qualify the competitive examinations.(c) /no error 8.

### Easy way to understand Direct and Indirect speech rules

Introduction. There two ways to convey a message of a person, or the words spoken by a person to other person. 1.       Direct speech 2.       Indirect speech Suppose your friend whose name is Vipul tells you in College , “I will give you a pen”. You come to home and you want to tell your brother what your friend told you. There are two ways to tell him. Direct speech:   Vipul said, “I will give you a pen”. Indirect Speech:  Vipul said that he would give me a pen. In direct speech   the original words of person are narrated (no change is made) and are enclosed in quotation mark. While in indirect speech some changes are made in original words of the person because these words have been spoken in past so the tense will change accordingly and pronoun may also be changed accordingly. In indirect speech  the statement of the person is not enclosed in quotation marks, the word “ that ” may be used before the statement to show that it is indirect sp