Maths :(

[abc123]

Can anyone please explain similarity and congruency? I never get that esp when you have to prove when two triangles are similiar or congruent with no info given. And also finding the area and volume of similiar figures? I know the formulas for it but in a case or two (I don't remember the questions) the lengths are not squared. Why?

 

[abcde]

AOA!
Post some specific questions. We might be able to help.

 

[ibadsiddiqi]

oh i love that topic!! and yes post some specific questions. Its a bit difficult to explain it properly without any examples

 

[Silent Hunter]

@ibadsiddiqi: there must be few points? can u tell those like when two triangles are congruent? or similar?

 

[ibadsiddiqi]

if the two triangles are congruent then it means that the two triangle have atleast three properties which are equal. There are three cases in which two triangles are said to be equal. E.g if all the angles of triangle ABC is are equal to the corresponding angles of triangle PQR then the two triangles are said to be equal (AAA). If ABC and PQR are two right angle triangles and side AB=PQ and side BC=QR then two triangles are said to be congruent (SAS). If two triangles have equal sides then they are said to be equal (SSS). Now for two triangles to be similar, the triangles need to have atleast three SIMILAR not SAME properties. For example if two triangles have different angles and lengths but the ratio of the lengths of the triangles are the same then the triangles are similar e.g in triangle ABC the height of the triangle AB is 4cm while in trianlge PQR the height of triangle PQ is cm. The base AC is 2cm and the base PR is 4cm. Here you can see that the size of the height and base of triangle ABC is in the ratio of 1:2 with the height and base of triangle PQR. therefore the two triangles are said to be similar. Now if you have to similar triangles and you have to similar triangles and you have to find the ratio of the their areas, you first of all find out the common side. E.g you have to find the ratio of area of triangle ABC to area of triangle ABR and they have a common base AB= 4cm and AR=2cm then the ratio of their areas is (4/2)^2

So these are the basics of congruency and similarity. In order for a more detailed explanation you have to give me a sample question. Anyways I hope you found this helpful.

 

[abcde]

Tests for CONGRUENCY:
1. If all three sides of one triangle are equal to the three sides of the other triangle, then the two triangles are congruent. (SSS Property)
2. If two sides and the included angle of one triangle are equal to the two sides and included angle of the other triangle, then the two triangles are congruent. (SAS Property)
3. If two angles and a side of one triangle are equal to two angles and the corresponding side of the other triangle, then the two triangles are congruent. (AAS Property)
4. If the hypotenuse and one side of a right-angled triangle are equal to the hypotenuse and one side of the other right-angled triangle, then the two right-angled triangles are congruent. (RHS Property)

Tests for SIMILARITY:
1. Two angles of one triangle are equal to the two angles of the other triangle. (AAA Property)
2. All the corresponding sides of the the two triangles are proportional.
3. The angle of one triangle is equal to the angle of the other triangle and the sides which include the equal angle of both triangles are proportional.

 

[abc123]

ibadsiddiqi there is a question in the june 2009 paper ques 19 http://www.xtremepapers.me/CIE/Cambridg ... 9_qp_1.pdf

for part a i could only figure out reason that angle A is common. Listen when finding out the area of similiar triangles when do we not square the lengths? I can't find those questions otherwise would have posted them

 

[abcde]

You do not 'square the lengths' when the base or height of the two triangles are equal. In that case, the ratio of their areas is simply the ratio of any two corresponding lengths of the two triangles.

 

[ibadsiddiqi]

It is given that LMQ=PNL, QMN= MNP and therefore angle LMN=angle LNM. Due to this we can see that triangle LMN is an isosceles triangle. Now we can see that angle QML= anglePLN because it is a common angle and side LM=LN as the triangle LMN is and isosceles triangle and its is already given that LMQ=PNL. So we can prove that the two triangles are congruent as they have one equal side and two equal angles i.e the (ASA) property.
Hope you got it

 

[ibadsiddiqi]

as for your other question, it has been perfectly answered but abcde.

 

[abc123]

yes i did i shall practise more sums on it now, hopefully will get them otherwise i will post them here tomm

 

[ibadsiddiqi]

sure. If you need any more help, just ask

 

[ibadsiddiqi]

abc123 try solving Q.4 from http://www.xtremepapers.me/CIE/Cambridg ... 4_qp_1.pdf
and Q.12 from http://www.xtremepapers.me/CIE/Cambridg ... 5_qp_1.pdf