Advertisements
Advertisements
Question
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
Solution
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 | ∆LMN | |
| 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. |
RELATED QUESTIONS
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.
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 an isosceles triangle whose base is 8 cm and altitude 4 cm and then another triangle whose side are `1 1/2` times the corresponding sides of the isosceles 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.
Divide a line segment of length 9 cm internally in the ratio 4 : 3. Also, give justification of the construction.
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 an isosceles triangle whose base is 8 cm and altitude 4 cm and then another triangle whose sides are 3/2 times the corresponding sides of the isosceles triangle.
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 line segment of length 7.6 cm and divide it in the ratio 5 : 8. Measure the two parts.
∆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`.
∆ABC ~ ∆LBN. In ∆ABC, AB = 5.1 cm, ∠B = 40°, BC = 4.8 cm, \[\frac{AC}{LN} = \frac{4}{7}\]. Construct ∆ABC and ∆LBN.
If A(–14, –10), B(6, –2) is given, find the coordinates of the points which divide segment AB into four equal 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`.
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.
Δ AMT ∼ ΔAHE. In Δ AMT, MA = 6.3 cm, ∠MAT = 120°, AT = 4.9 cm, `(MA)/(HA) = 7/5`. construct Δ AHE.
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.
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:
ΔRHP ~ ΔNED, In ΔNED, NE = 7 cm, ∠D = 30°, ∠N = 20° and `"HP"/"ED" = 4/5`. Then construct ΔRHP and ΔNED
ΔRHP ~ ΔNED, In ΔNED, NE = 7 cm, ∠D = 30°, ∠N = 20°, `(HP)/(ED) = 4/5`, then construct ΔRHP and ∆NED.
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 `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 ______.
By geometrical construction, it is possible to divide a line segment in the ratio ______.
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 ______.
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?
A point C divides a line segment AB in the ratio 5 : 6. The ratio of lengths AB: BC is ______.
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 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 ______.
Draw a triangle ABC in which BC = 6 cm, CA = 5 cm and AB = 4 cm. Construct a triangle similar to it and of scale factor `5/3`.
Draw an isosceles triangle ABC in which AB = AC = 6 cm and BC = 5 cm. Construct a triangle PQR similar to ∆ABC in which PQ = 8 cm. Also justify the construction.
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 cm and divide it in the ratio 5 : 3.
