Question

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Answer 6 questions perfectly with quality and well explained!

Questions:

Q.1. Draw an acute angled Triangle PQR. Draw all of it's altitudes. Name the point of concurrence as "O"

Q.2. Draw an obtuse angled Triangle STV. Draw it's medians and show the centroid.

Q.3. Draw an obtuse angled Triangle LMN. Draw it's altitudes and denote the orthocentre by "O".

Q.4. Draw an obtuse angled Triangle XYZ . Draw it's medains and show their point of concurrence by G.

Q.5 Draw an isosceles triangle. Draw all of it's medains and altitudes. Write your observation about their points of concurrence.
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Q.6 Fill in the Balnks! is in the Attachment!
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Answer 1

Answers :

1) Draw an acute angled traingle PQR . Draw all of its altitude . Name the point of concurrence as "O".

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1. Draw an acute angled triangle PQR
2. With P as the center draw an arc cutting a side of QR.
3. Take x as the center and measure more radius than the half length of xy and draw an arc below QR.
4. Now take y is the centre and with the same radius of half length more than xy ; draw an Arc that cuts through the another arc that was formed with the previous step.
5. Now join PA which intersect the line QR and name all of their common intersection point as L.
6. This makes PL the altitude.
7. Now if we draw QM on the line PR ; QM become its attitude.
8. Then drawing RC on line PQ makes it the the altitude.

So , we have got :

∆ PQR

Altitude : PL , QM , RC

2) Draw an obtuse angle angle triangle STV. Draw its medians and show the centroid.

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1. Draw an obtuse angled triangle STV.
2. Draw a bisector to the side of TV intersecting at L. It is the mid point.
3. Join SL . SL is median to side of TV.
4. So we get midpoints of : SV - M and ST - N
5. Join VN to TV , ST and SV intersecting at G. This is it's centroid.

3) Draw an obtuse angle triangle LMN and draw its attitudes and denote the orthocenter by O.

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1. Draw an obtuse angle triangle LMN.
2. Take L as the centre and draw 2 arcs intersecting MN at point P and Q.
3. Consider P as the centre and take a radius of more than half length of PQ . Draw arc . Now take Q as the centre and with the same radius draw an Arc are that is cutting through the previous arc formed.
4. Draw LR intersecting at MN at I .
5. LI is the altitude to side of MN.
6. Extend NL till point V
7. Take M as the center and draw arc intersecting NL
8. Take D as the centre and radius hs more than half length of DE , drawing an arc. Take E as a centre and same radius draw another arc intersecting the previous one at F.
9. Join MF intersecting NL . Name this K
10. MK is altitude of NL.
11. Extend ML to U
12. Take N as centre and draw two arcs intersecting ML at A and B.
13. Consider A as centre and radius more than half of AB draw arc. Taking B as centre and same radius draw another arc intersecting the previous one at C
14. Join NC at ML . Name this as J
15. NJ is altitude to ML

4) Draw an right angle triangle XYZ . Draw its median and show point of congruence by G.

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1. Draw right angle triangle XYZ
2. Draw perpendicular bisector at PQ on YZ and intersect at L.
3. Join XL. XL makes median of YZ
4. Make a perpendicular bisector TU to side ZX with intersecting XY at M.
5. Join YM. YM is median to ZX
6. Draw bisector RS to XY intersecting XY at N.
7. Join ZN . ZN is median to XY.

5) Draw an isosceles triangle . Draw medians and altitudes . Write observation about points of congruence.

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1. Draw isosceles triangle XYZ
2. Draw perpendicular bisector DE of side YZ that intersect at L.
3. Join XL. XL is the median to YZ
4. With X as the centre draw two arcs intersecting YZ at A and B.
5. With center as A take length more than half of AB and draw an arc. Taking B as the centre and same radius draw another arc intersecting the previous one at C.
6. Join XC intersecting at YZ at L. XL is altitude of YZ.
7. Draw perpendicular bisector IJ intersect ZX at K
8. Join YK. YK is median to ZX
9. Y as centre now draw two arcs intersecting ZX at Z and F. Now taking Z as centre and radius of half more than ZF draw an arc . With F as centre and same radius draw another arc cutting through the previous one at H.
10. Join YH intersect ZX at M. YM is altitude to ZX
11. Draw perpendicular bisector ST at XY intersecting at U.
12. Join ZU . Thus median of XY
13. With Z as cetre and draw two arcs intersecting XY at P and Q.
14. With P as centre and radius of half more than PQ draw an Arc. Now taking Q as the centre and same radius draw another are intersecting on cutting the previous one at R.
15. Join ZR intersecting at XY and Name it N. ZN is altitude of XY.

Here point G is the centroid and orthocentre of ∆XYZ .

Observation : In an isosceles triangle centroid and orthocentre lie on same straight line.

6) Answers :

1. If RG is 2.5 then GC is 5.
2. If BG is 6 then BQ is 9.
3. If AP is 6 then AG is 4 and GP is 2.

Answer 2

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For all 5 question refer to the attachments !

question 6 :

a) If (RG) = 2.5 then l (GC) = 5

b) if (BG) = 6 then l (BQ) = 9

c) if (AP) = 6 then l (AG) = 4 and l (GP) = 2

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