Maths congruence question3

[ana_mujahid]

4) PQRS is a square and equilateral triangles PQA and RQB are drawn with A inside and B outside the square.
By considering triangles PQR and AQB, prove that AB is equal to PR



how does the shape look like,

use paint or somfink and attach please :)


thanks

need today (3hours max)

[Ibn Al-Jarrah]

P __________ R
|\ |\
| \ | \ B
| / A | /
|/__________|/
Q S


the triangles all have 60 degree angles

since PR is a straight line, and angle A and B are equal, they will both be parallel

[ana_mujahid]

P __________ R
|\ |\
| \ | \ B
| / A | /
|/__________|/
Q S


the triangles all have 60 degree angles

since PR is a straight line, and angle A and B are equal, they will both be parallel

can u use paint and upload it, or send it to me on msn (ill pm if u want) cuz i cant see it

[mizfissy815]

Should look something like that I reckon...

My reasoning is slightly different to Ibn Jarrah's.

Since PRQ is an isosceles triangle where PR=PQ (with QR as the hypotenuse of that triangle) and PQA is an equilateral triangle, where PQ=QA=PA....QA= PR.

Since QRB is an equilateral, QR=QB=BR ....QAB is also an isosceles triangle, where QA=AB...


AB=PR.

You could alternatively use the angles argument.

[ana_mujahid]

Should look something like that I reckon...

My reasoning is slightly different to Ibn Jarrah's.

Since PRQ is an isosceles triangle where PR=PQ (with QR as the hypotenuse of that triangle) and PQA is an equilateral triangle, where PQ=QA=PA....QA= PR.

Since QRB is an equilateral, QR=QB=BR ....QAB is also an isosceles triangle, where QA=AB...


AB=PR.

You could alternatively use the angles argument.


so wat congruent rule is it? SAS?

[mizfissy815]

so wat congruent rule is it? SAS?

Edit- No, you're right it is SAS.

[ana_mujahid]

i c


thanks Ibn Jarrah and mizfissy

[mizfissy815]

Ok, take a look at this pic.

Ignoring everything else, triangle PRQ is an isosceles where angle PQR and PRQ = 45...(since angle QPR is clearly 90.)

We already know that PQ = QA....and QR =AB and the angle between QA and QB is also 45. So, AB = PR and the rule is SAS.

[ana_mujahid]

Ok, take a look at this pic.

Ignoring everything else, triangle PRQ is an isosceles where angle PQR and PRQ = 45...(since angle QPR is clearly 90.)

We already know that PQ = QA....and QR =AB and the angle between QA and QB is also 45. So, AB = PR and the rule is SAS.

:up:

:jkk: sister :)