Advertisements
Advertisements
प्रश्न
ΔRHP ~ ΔNED, In ΔNED, NE = 7 cm, ∠D = 30°, ∠N = 20°, `(HP)/(ED) = 4/5`, then construct ΔRHP and ∆NED.
Advertisements
उत्तर
Analysis:
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`
∴ RH = 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. |
APPEARS IN
संबंधित प्रश्न
Draw a line segment of length 7.6 cm and divide it in the ratio 5:8. Measure the two parts. Give the justification of the construction.
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 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 line segment of length 7 cm and divide it internally in the ratio 2 : 3.
Construct a triangle similar to a given ΔABC such that each of its sides is (2/3)rd of the corresponding sides of ΔABC. It is given that BC = 6 cm, ∠B = 50° and ∠C = 60°.
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 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.
Find the ratio in which point P(k, 7) divides the segment joining A(8, 9) and B(1, 2). Also find k.
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`.
______ number of tangents can be drawn to a circle from the point on the circle.
Draw seg AB of length 9 cm and divide it in the ratio 3 : 2.
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 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 ______.
A rhombus ABCD in which AB = 4cm and ABC = 60o, divides it into two triangles say, ABC and ADC. Construct the triangle AB’C’ similar to triangle ABC with scale factor `2/3`. Select the correct figure.
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′.
If the perpendicular distance between AP is given, which vertices of the similar triangle would you find first?
A point C divides a line segment AB in the ratio 5 : 6. The ratio of lengths AB: BC is ______.
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.
