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 | ∆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. |
RELATED QUESTIONS
Construct a Δ ABC in which AB = 6 cm, ∠A = 30° and ∠B = 60°, Construct another ΔAB’C’ similar to ΔABC with base AB’ = 8 cm.
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 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
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 line segment of length 7 cm and divide it internally in the ratio 2 : 3.
Divide a line segment of length 14 cm internally in the ratio 2 : 5. Also, justify your construction.
Draw a ΔABC in which BC = 6 cm, AB = 4 cm and AC = 5 cm. Draw a triangle similar to ΔABC with its sides equal to (3/4)th of the corresponding sides of ΔABC.
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.
Construct a triangle similar to ΔABC in which AB = 4.6 cm, BC = 5.1 cm, ∠A = 60° with scale factor 4 : 5.
Draw a triangle ABC with side BC = 6 cm, ∠C = 30° and ∠A = 105°. Then construct another triangle whose sides are `2/3` times the corresponding sides of ΔABC.
∆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 (20, 10), B(0, 20) are given, find the coordinates of the points which divide segment AB into five congruent parts.
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.
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.
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.
Choose the correct alternative:
∆ABC ∼ ∆AQR. `"AB"/"AQ" = 7/5`, then which of the following option is true?
ΔAMT ~ ΔAHE. In ΔAMT, AM = 6.3 cm, ∠MAT = 120°, AT = 4.9 cm, `"AM"/"HA" = 7/5`, then construct ΔAMT and ΔAHE
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 p : q (p, q are positive integers), draw a ray AX so that ∠BAX is an acute angle and then mark points on ray AX at equal distances such that the minimum number of these points 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 divide a line segment AB in the ratio 5 : 6, draw a ray AX such that ∠BAX is an acute angle, then draw a ray BY parallel to AX and the points A1, A2, A3, ... and B1, B2, B3, ... are located at equal distances on ray AX and BY, respectively. Then the points joined are ______.
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 triangle ABC is such that BC = 6cm, AB = 4cm and AC = 5cm. For the triangle similar to this triangle with its sides equal to `3/4`th of the corresponding sides of ΔABC, correct figure is?
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′.
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. |
The image of construction of A’C’B a similar triangle of ΔACB is given below. Then choose the correct option.
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?
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.
To divide a line segment, the ratio of division must be ______.
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 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 AB of length 6 cm and mark a point X on it such that AX = `4/5` AB. [Use a scale and compass]
