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Answer 1

Question :

Draw an isosceles triangle . Draw all of its medians and altitudes . Write your observation about their points of congruence.

Answer :

1. Draw an isosceles ∆XYZ
2. Draw the perpendicular bisector DE of side YZ that intersect YZ at L
3. Join XL . XL is the median to side YZ.
4. With X as the centre draw two arcs intersecting YZ at A and B .
5. Now take A as the new centre and radius more than half of the value of AB draw an arc . Now draw another arc cutting through the previous arc . Name the point as C.
6. Join XC intersecting YZ at L.
7. XL is altitude to YZ.
8. Now draw another perpendicular bisector as IJ on side ZX intersecting ZX . Name intersecting point as K.
9. Join YK
10. YK is median to ZX
11. With Y as centre draw two arcs each intersecting Z and F .
12. Now take Z as new centre and radius more than half of ZF draw an arc.
13. With F as centre and same radius draw another arc cutting through the previous one.
14. Name the point as H.
15. Join YH on the point which ZX intersect as M.
16. YM is altitude of ZX.
17. Draw perpendicular bisector ST beside XY Intersecting XY at U.
18. Join ZU .
19. ZU Is median to XY
20. Take Z as centre and draw two arcs intersecting XY at P and Q.
21. Take P as the centre and radius more than half of PQ ; draw an arc.
22. Now take Q as the centre and same radius draw another arc cutting through the previous one.
23. Name it R.
24. Join ZR Intersecting XY at N .
25. ZN is altitude to XY

Observation :

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

• Isosceles triangle : ∆XYZ

• Medians and their sides :

1. XL - YZ
2. YK - ZX
3. ZU - XY

• Intersection point : G

• Altitude and sides :

1. XL - YZ
2. YM - ZX
3. ZN - XY

Answer 2

Answer:

the correct answer is above