Advertisements
Advertisements
प्रश्न
ΔRHP ~ ΔNED, In ΔNED, NE = 7 cm, ∠D = 30°, ∠N = 20° and `"HP"/"ED" = 4/5`. Then construct ΔRHP and ΔNED
Advertisements
उत्तर
In ∆NED, ∠D = 30°
and ∠N = 20° ......(i) [Given]
∴ ∠E = 130° .....(ii) [Remaining angle of a triangle]
∆RHP ∼ ∆NED
∴ `"RH"/"NE" = "HP"/"ED" = "PR"/"DN"` .....[Corresponding sides of similar triangles]
∴ `"RH"/7 = 4/5` ......[Given]
∴ RH = `(4 xx 7)/5` = 5.6 cm
Also, ∠R = ∠N, ∠H = ∠E, ∠P = ∠D ......(iii) [Corresponding angles of similar triangles]
∴ ∠R = 20°, ∠H = 130°, ∠P = 30° ......[From (i),(ii) and (iii)]
Steps of Construction:
| ∆NED | ∆RHP | |
| i. | Draw seg NE of 7 cm | Draw seg RH of 5.6 cm |
| ii. | Draw a ray NA and EB such that ∠ANE = 20° and ∠BEN = 130°. | Draw a ray RC and HD such that ∠CRH = 20° and ∠DHR = 130°. |
| iii. | Name the point of intersection of rays D. | Name the point of intersection of rays P. |
संबंधित प्रश्न
Write down the equation of a line whose slope is 3/2 and which passes through point P, where P divides the line segment AB joining A(-2, 6) and B(3, -4) in the ratio 2 : 3.
ΔRST ~ ΔUAY, In ΔRST, RS = 6 cm, ∠S = 50°, ST = 7.5 cm. The corresponding sides of ΔRST and ΔUAY are in the ratio 5 : 4. Construct ΔUAY.
Construct the circumcircle and incircle of an equilateral triangle ABC with side 6 cm and centre O. Find the ratio of radii of circumcircle and incircle.
Find the ratio in which the line segment joining the points A(3,- 3) and B(- 2, 7) is divided by x-axis. Also find the coordinates of the point of division.
Construct a triangle with sides 5 cm, 6 cm and 7 cm and then another triangle whose sides are `7/5` of the corresponding sides of the first triangle. Give the justification of the construction.
Draw a right triangle in which the sides (other than hypotenuse) are of lengths 4 cm and 3 cm. the construct another triangle whose sides are `5/3` times the corresponding sides of the given 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.
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 right triangle in which the sides (other than hypotenuse) are of lengths 5 cm and 4 cm. Then construct another triangle whose sides are 5/3th times the corresponding sides of the given triangle.
Construct a ΔABC in which AB = 5 cm. ∠B = 60° altitude CD = 3cm. Construct a ΔAQR similar to ΔABC such that side ΔAQR is 1.5 times that of the corresponding sides of ΔACB.
Draw a right triangle in which sides (other than the hypotenuse) are of lengths 8 cm and 6 cm. Then construct another triangle whose sides are 3/4 times the corresponding sides of the first triangle.
Construct the circumcircle and incircle of an equilateral ∆XYZ with side 6.5 cm and centre O. Find the ratio of the radii of incircle and circumcircle.
Construct a right triangle in which the sides, (other than the hypotenuse) are of length 6 cm and 8 cm. Then construct another triangle, whose sides are `3/5` times the corresponding sides of the given triangle.
∆AMT ~ ∆AHE. In ∆AMT, AM = 6.3 cm, ∠TAM = 50°, AT = 5.6 cm, `(AM)/(AH) = 7/5`. Construct ∆AHE.
Construct ∆PYQ such that, PY = 6.3 cm, YQ = 7.2 cm, PQ = 5.8 cm. If \[\frac{YZ}{YQ} = \frac{6}{5},\] then construct ∆XYZ similar to ∆PYQ.
Find the ratio in which point P(k, 7) divides the segment joining A(8, 9) and B(1, 2). Also find k.
If A(–14, –10), B(6, –2) is given, find the coordinates of the points which divide segment AB into four equal 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 line segment AB of length 7 cm. Using ruler and compasses, find a point P on AB such that `(AP)/(AB)=3/5`.
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.
Points P and Q trisect the line segment joining the points A(−2, 0) and B(0, 8) such that P is near to A. Find the coordinates of points P and Q.
In the figure ΔABC ~ ΔADE then the ratio of their corresponding sides is:
ΔPQR ~ ΔABC. In ΔPQR, PQ = 3.6 cm, QR = 4 cm, PR = 4.2 cm. Ratio of the corresponding sides of triangle is 3 : 4, then construct ΔPQR 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.
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 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 ______.
To construct a triangle similar to a given ΔABC with its sides `8/5` of the corresponding sides of ΔABC draw a ray BX such that ∠CBX is an acute angle and X is on the opposite side of A with respect to BC. Then minimum number of points to be located at equal distances on ray BX is ______.
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 ______.
When a line segment is divided in the ratio 2 : 3, how many parts is it divided into?
Match the following based on the construction of similar triangles, if scale factor `(m/n)` is.
| Column I | Column II | ||
| i | >1 | a) | The similar triangle is smaller than the original triangle. |
| ii | <1 | b) | The two triangles are congruent triangles. |
| iii | =1 | c) | The similar triangle is larger than the original 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 ______.
Two line segments AB and AC include an angle of 60° where AB = 5 cm and AC = 7 cm. Locate points P and Q on AB and AC, respectively such that AP = `3/4` AB and AQ = `1/4` AC. Join P and Q and measure the length PQ.
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.
