Advertisements
Advertisements
प्रश्न
ΔABC ~ ΔPBR, BC = 8 cm, AC = 10 cm , ∠B = 90°, `"BC"/"BR" = 5/4` then construct ∆ABC and ΔPBR
उत्तर
Analysis: In ∆ABC, ∠B = 90° ......[Given]
∴ AC2 = AB2 + BC2 ......[Pythagoras theorem]
∴ 102 = AB2 + 82
∴ AB2 = 100 – 64
∴ AB2 = 36
∴ AB = 6 cm ......[Taking square root of both sides]
Steps of construction:
- Draw seg BC of length 8 cm.
- Take ∠B as 90° and draw an arc of 6 cm on it. Name the point as A.
- Join seg AC to obtain ∆ABC.
- Draw ray BX such that ∠CBX is an acute angle.
- Locate points B1, B2, B3, B4, B5 on ray BX such that, BB1 = B1B2 = B2B3 = B3B4 = B4B5.
- Join point C and B5.
- Through point B4 draw a line parallel to seg CB5 which intersects seg BC at point R.
- Draw a line parallel to AC through R to intersect line AB at point P.
∆PBR is the required triangle similar to ∆ABC.
APPEARS IN
संबंधित प्रश्न
Construct a triangle ABC in which AB = 5 cm, BC = 6 cm and ∠ABC = 60˚. Now construct another triangle whose sides are 5/7 times the corresponding sides of ΔABC.
Draw a triangle ABC with BC = 7 cm, ∠B = 45° and ∠A = 105°. Then construct a triangle whose sides are`4/5` times the corresponding sides of ΔABC.
Construct a triangle of sides 4 cm, 5cm and 6cm and then a triangle similar to it whose sides are `2/3` of the corresponding sides of the first triangle. Give the justification of the construction.
Construct an isosceles triangle with base 8 cm and altitude 4 cm. Construct another triangle whose sides are `2/3` times the corresponding sides of the isosceles triangle.
Construct a triangle similar to a given ΔXYZ with its sides equal to (3/4)th of the corresponding sides of ΔXYZ. Write the steps of construction.
Draw a triangle ABC with side BC = 6 cm, ∠C = 30° and ∠A = 105°. Then construct another triangle whose sides are `2/3` times the corresponding sides of ΔABC.
∆AMT ~ ∆AHE. In ∆AMT, AM = 6.3 cm, ∠TAM = 50°, AT = 5.6 cm. `"AM"/"AH" = 7/5`. Construct ∆AHE.
Find the ratio in which point P(k, 7) divides the segment joining A(8, 9) and B(1, 2). Also find k.
Find the co-ordinates of the points of trisection of the line segment AB with A(2, 7) and B(–4, –8).
If A (20, 10), B(0, 20) are given, find the coordinates of the points which divide segment AB into five congruent parts.
Given A(4, –3), B(8, 5). Find the coordinates of the point that divides segment AB in the ratio 3 : 1.
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 \[\frac{3}{5}\] times the corresponding sides of the given triangle.
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.
Choose the correct alternative:
In the figure ΔABC ~ ΔADE then the ratio of their corresponding sides is ______
Choose the correct alternative:
ΔPQR ~ ΔABC, `"PR"/"AC" = 5/7`, then
Draw seg AB of length 9 cm and divide it in the ratio 3 : 2
Construct an equilateral ∆ABC with side 5 cm. ∆ABC ~ ∆LMN, ratio the corresponding sides of triangle is 6 : 7, then construct ΔLMN and ΔABC
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`
To divide a line segment AB in the ratio p : q (p, q are positive integers), draw a ray AX so that ∠BAX is an acute angle and then mark points on ray AX at equal distances such that the minimum number of these points is ______.
To divide a line segment AB in the ratio 4 : 7, a ray AX is drawn first such that ∠BAX is an acute angle and then points A1, A2, A3, .... are located at equal distances on the ray AX and the point B is joined to ______.
A triangle ABC is such that BC = 6cm, AB = 4cm and AC = 5cm. For the triangle similar to this triangle with its sides equal to `3/4`th of the corresponding sides of ΔABC, correct figure is?
To divide a line segment PQ in the ratio 5 : 7, first a ray PX is drawn so that ∠QPX is an acute angle and then at equal distances points are marked on the ray PX such that the minimum number of these points is ______.
The ratio of corresponding sides for the pair of triangles whose construction is given as follows: Triangle ABC of dimensions AB = 4cm, BC = 5 cm and ∠B= 60°.A ray BX is drawn from B making an acute angle with AB.5 points B1, B2, B3, B4 and B5 are located on the ray such that BB1 = B1B2 = B2B3 = B3B4 = B4B5.
B4 is joined to A and a line parallel to B4A is drawn through B5 to intersect the extended line AB at A’.
Another line is drawn through A’ parallel to AC, intersecting the extended line BC at C’. Find the ratio of the corresponding sides of ΔABC and ΔA′BC′.
Construction of similar polygons is similar to that of construction of similar triangles. If you are asked to construct a parallelogram similar to a given parallelogram with a given scale factor, which of the given steps will help you construct a similar parallelogram?
What is the ratio `(AC)/(BC)` for the following construction: A line segment AB is drawn. A single ray is extended from A and 12 arcs of equal lengths are cut, cutting the ray at A1, A2… A12.A line is drawn from A12 to B and a line parallel to A12B is drawn, passing through the point A6 and cutting AB at C.
The basic principle used in dividing a line segment is ______.
By geometrical construction, it is possible to divide a line segment in the ratio `sqrt(3) : 1/sqrt(3)`.
To construct a triangle similar to a given ∆ABC with its sides `7/3` of the corresponding sides of ∆ABC, draw a ray BX making acute angle with BC and X lies on the opposite side of A with respect to BC. The points B1, B2, ...., B7 are located at equal distances on BX, B3 is joined to C and then a line segment B6C' is drawn parallel to B3C where C' lies on BC produced. Finally, line segment A'C' is drawn parallel to AC.
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 triangle ABC in which AB = 5 cm, BC = 6 cm and ∠ABC = 60°. Construct a triangle similar to ∆ABC with scale factor `5/7`. Justify the construction.
Draw a line segment AB of length 10 cm and divide it internally in the ratio of 2:5 Justify the division of line segment AB.
