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प्रश्न
Construct an isosceles triangle whose base is 8 cm and altitude 4 cm and then another triangle whose sides are 3/2 times the corresponding sides of the isosceles triangle.
उत्तर
Steps to construct
1. Draw a line segment BC of 8 cm
2. Take a mid point D of BC
3. At D, draw an angler of 90°
4.With centre D,Radius 4cm, draw an arc which intersect line of angle at A
5. Join AB and AC
6. At B, draw an angle CBX of any measure
7. Starting from B, cut there equal parts on BX such that BX1 = X1X2 = X2X3
8. Join X2C
9. Through X3, Draw X3Q || X2C
10. Through Q, Draw QP || CA
∴ ΔPBQ ∼ ΔABC
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संबंधित प्रश्न
Draw a line segment of length 7 cm and divide it internally in the ratio 2 : 3.
Draw a right triangle in which the sides (other than the hypotenuse) are of lengths 4 cm and 3 cm. Now construct another triangle whose sides are `3/5` times the corresponding sides of the given triangle.
Draw a line segment AB of length 7 cm. Using ruler and compasses, find a point P on AB such that `(AP)/(AB) = 3/5 `.
Find the co-ordinates of the points of trisection of the line segment AB with A(2, 7) and B(–4, –8).
Draw seg AB of length 9.7 cm. Take a point P on it such that A-P-B, AP = 3.5 cm. Construct a line MN ⊥ sag AB through point P.
ΔAMT ~ ΔAHE. In ΔAMT, AM = 6.3 cm, ∠MAT = 120°, AT = 4.9 cm, `"AM"/"HA" = 7/5`, then construct ΔAMT and ΔAHE
If the point P (6, 7) divides the segment joining A(8, 9) and B(1, 2) in some ratio, find that ratio
Solution:
Point P divides segment AB in the ratio m: n.
A(8, 9) = (x1, y1), B(1, 2 ) = (x2, y2) and P(6, 7) = (x, y)
Using Section formula of internal division,
∴ 7 = `("m"(square) - "n"(9))/("m" + "n")`
∴ 7m + 7n = `square` + 9n
∴ 7m – `square` = 9n – `square`
∴ `square` = 2n
∴ `"m"/"n" = square`
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Draw a parallelogram ABCD in which BC = 5 cm, AB = 3 cm and ∠ABC = 60°, divide it into triangles BCD and ABD by the diagonal BD. Construct the triangle BD' C' similar to ∆BDC with scale factor `4/3`. Draw the line segment D'A' parallel to DA where A' lies on extended side BA. Is A'BC'D' a parallelogram?
Draw a line segment of length 7.5 cm and divide it in the ratio 1:3.
