Advertisements
Advertisements
प्रश्न
Construct an equilateral ∆ABC with side 5 cm. ∆ABC ~ ∆LMN, ratio the corresponding sides of triangle is 6 : 7, then construct ΔLMN and ΔABC
Advertisements
उत्तर
Analysis: ∆ABC ∼ ∆LMN
∴ `"AB"/"LM" = "BC"/"MN" = "AC"/"LN"` ......[Corresponding sides of similar triangles]
∴ `5/"LM" = 5/"MN" = 5/"LN" = 6/7` .....[Given]
∴ `5/"LM" = 6/7`
∴ LM = `(5 xx 7)/6`
∴ LM = 5.8 cm (approx)
∴ LM = MN = LN = 5.8 cm (approx) .....[Equilateral triangle]
Steps of Construction:
| ∆ABC | ∆PQR | |
| i. | Draw seg BC of 5 cm | Draw seg MN of 5.8 cm |
| ii. | Draw two arcs at 5 cm from point B and point C respectively. | Draw two arcs at 5.8 cm from point M and point N respectively. |
| iii. | Name the point of intersection of two arcs as A. | Name the point of intersection of two arcs as L. |
| iv. | Join seg AB and seg AC. | Join seg LM and seg LN. |
संबंधित प्रश्न
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.
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.
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.
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.
Determine a point which divides a line segment of length 12 cm internally in the ratio 2 : 3 Also, justify your construction.
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.
∆PQR ~ ∆LTR. In ∆PQR, PQ = 4.2 cm, QR = 5.4 cm, PR = 4.8 cm. Construct ∆PQR and ∆LTR, such that `"PQ"/"LT" = 3/4`.
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(–14, –10), B(6, –2) is given, find the coordinates of the points which divide segment AB into four equal parts.
If A (20, 10), B(0, 20) are given, find the coordinates of the points which divide segment AB into five congruent parts.
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 AMT ∼ ΔAHE. In Δ AMT, MA = 6.3 cm, ∠MAT = 120°, AT = 4.9 cm, `(MA)/(HA) = 7/5`. construct Δ AHE.
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.
Choose the correct alternative:
______ number of tangents can be drawn to a circle from the point on the circle.
ΔABC ~ ΔPBR, BC = 8 cm, AC = 10 cm , ∠B = 90°, `"BC"/"BR" = 5/4` then construct ∆ABC and ΔPBR
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 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 `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 ______.
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 ______.
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.
For ∆ABC in which BC = 7.5cm, ∠B =45° and AB - AC = 4, select the correct figure.
Draw the line segment AB = 5cm. From the point A draw a line segment AD = 6cm making an angle of 60° with AB. Draw a perpendicular bisector of AD. Select the correct figure.
When a line segment is divided in the ratio 2 : 3, how many parts is it divided into?
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?
The point W divides the line XY in the ratio m : n. Then, the ratio of lengths of the line segments XY : WX is ______.
What is the ratio `(AC)/(BC)` for the line segment AB following the construction method below?
Step 1: A ray is extended from A and 30 arcs of equal lengths are cut, cutting the ray at A1, A2,…A30
Step 2: A line is drawn from A30 to B and a line parallel to A30B is drawn, passing through the point A17 and meet AB at C.
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 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 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.
