Advertisements
Advertisements
प्रश्न
ΔABC ~ ΔPBR, BC = 8 cm, AC = 10 cm, ∠B = 90°, `(BC)/(BR) = 5/4` then construct ∆ABC and ΔPBR.
Advertisements
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.
Construct a triangle ABC in which BC = 6 cm, AB = 5 cm and ∠ABC = 60°. Then construct another triangle whose sides are`3/4` 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 ABC with BC = 7 cm, ∠B = 60° and AB = 6 cm. Construct another triangle whose sides are `3/4` times the corresponding sides of ∆ABC.
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.
Determine a point which divides a line segment of length 12 cm internally in the ratio 2 : 3 Also, justify your construction.
Construct a triangle similar to a given ΔABC such that each of its sides is (5/7)th of the corresponding sides of Δ ABC. It is given that AB = 5 cm, BC = 7 cm and ∠ABC = 50°.
Draw a right triangle ABC in which AC = AB = 4.5 cm and ∠A = 90°. Draw a triangle similar to ΔABC with its sides equal to (5/4)th of the corresponding sides of ΔABC.
Find the ratio in which point T(–1, 6)divides the line segment joining the points P(–3, 10) and Q(6, –8).
If A (20, 10), B(0, 20) are given, find the coordinates of the points which divide segment AB into five congruent parts.
The line segment AB is divided into five congruent parts at P, Q, R and S such that A–P–Q–R–S–B. If point Q(12, 14) and S(4, 18) are given find the coordinates of A, P, R, B.
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`.
Δ SHR ∼ Δ SVU. In Δ SHR, SH = 4.5 cm, HR = 5.2 cm, SR = 5.8 cm and
SHSV = 53 then draw Δ SVU.
Find the co-ordinates of the centroid of the Δ PQR, whose vertices are P(3, –5), Q(4, 3) and R(11, –4)
Find the ratio in which the segment joining the points (1, –3) and (4, 5) is divided by the x-axis? Also, find the coordinates of this point on the x-axis.
______ number of tangents can be drawn to a circle from the point on the circle.
ΔRHP ~ ΔNED, In ΔNED, NE = 7 cm, ∠D = 30°, ∠N = 20° and `"HP"/"ED" = 4/5`. Then construct ΔRHP and ΔNED
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`
Point P divides the line segment joining R(-1, 3) and S(9,8) in ratio k:1. If P lies on the line x - y + 2 = 0, then value of k is ______.
To divide a line segment AB in the ratio 5 : 7, first a ray AX is drawn so that ∠BAX is an acute angle and then at equal distances points are marked on the ray AX such that the minimum number of these points is ______.
To construct a triangle similar to a given ΔABC with its sides `3/7` of the corresponding sides of ΔABC, first draw a ray BX such that ∠CBX is an acute angle and X lies on the opposite side of A with respect to BC. Then locate points B1, B2, B3, ... on BX at equal distances and next step is to join ______.
By geometrical construction, it is possible to divide a line segment in the ratio ______.
For ∆ABC in which BC = 7.5cm, ∠B =45° and AB - AC = 4, select the correct figure.
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 ______.
If you need to construct a triangle with point P as one of its vertices, which is the angle that you need to construct a side of the triangle?
If a triangle similar to given ΔABC with sides equal to `3/4` of the sides of ΔABC is to be constructed, then the number of points to be marked on ray BX is ______.
To divide a line segment, the ratio of division must be ______.
By geometrical construction, it is possible to divide a line segment in the ratio `sqrt(3) : 1/sqrt(3)`.
Draw a line segment of length 7 cm. Find a point P on it which divides it in the ratio 3:5.
Draw a triangle ABC in which AB = 4 cm, BC = 6 cm and AC = 9 cm. Construct a triangle similar to ∆ABC with scale factor `3/2`. Justify the construction. Are the two triangles congruent? Note that all the three angles and two sides of the two triangles are equal.
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.
Draw a line segment of length 7.5 cm and divide it in the ratio 1:3.
Draw a line segment of length 7 cm and divide it in the ratio 5 : 3.
Draw a line segment AB of length 6 cm and mark a point X on it such that AX = `4/5` AB. [Use a scale and compass]
