Advertisements
Advertisements
प्रश्न
∆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`.
Advertisements
उत्तर
Rough figure:
Steps of construction:
- Draw ΔPQR such that PQ = 4.2 cm, QR = 5.4 cm and PR = 4.8 cm.
- Draw a ray at point R, making a suitable angle with seg RQ.
- Take equal parts RR1, R1R2, R2R3, R3R4 on ray RX.
- Join the points Q and R3.
- Draw seg TR4 || seg QR3.
- Draw seg LT || seg PQ.
Construction:
Notes
- For drawing ΔPRQ of given measures = 1 mark
- For drawing acute angle at point R = 0.5 mark
- To mark points R1, R2, R3, R4 on ray RX at equal distance from point R = 0.5 mark
- To join seg R3Q and to draw parallel seg R4T to seg R3Q = 0.5 mark
- To draw parallel seg to PQ at point T = 0.5 mark
APPEARS IN
संबंधित प्रश्न
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 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 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.
Divide a line segment of length 9 cm internally in the ratio 4 : 3. Also, give justification of the construction.
Divide a line segment of length 14 cm internally in the ratio 2 : 5. Also, justify your 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 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 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.
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.
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.
If A (20, 10), B(0, 20) are given, find the coordinates of the points which divide segment AB into five congruent parts.
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.
∆ABC ∼ ∆AQR. `(AB)/(AQ) = 7/5`, then which of the following option is true?
∆ABC ~ ∆PBQ. In ∆ABC, AB = 3 cm, ∠B = 90°, BC = 4 cm. Ratio of the corresponding sides of two triangles is 7 : 4. Then construct ∆ABC and ∆PBQ.
Construct an equilateral ∆ABC with side 5 cm. ∆ABC ~ ∆LMN, ratio the corresponding sides of triangle is 6 : 7, then construct ΔLMN and ΔABC.
ΔRHP ~ ΔNED, In ΔNED, NE = 7 cm, ∠D = 30°, ∠N = 20°, `(HP)/(ED) = 4/5`, then construct ΔRHP and ∆NED.
ΔABC ~ ΔPBR, BC = 8 cm, AC = 10 cm, ∠B = 90°, `(BC)/(BR) = 5/4` then construct ∆ABC and ΔPBR.
If the point P(6, 7) divides the segment joining A(8, 9) and B(1, 2) in some ratio, find that ratio.
Solution:
Point P divides segment AB in the ratio m : n.
A(8, 9) = (x1, y1), B(1, 2) = (x2, y2) and P(6, 7) = (x, y)
Using Section formula of internal division,
∴ `7 = (m(square) - n(9))/(m + n)`
∴ 7m + 7n = `square` + 9n
∴ 7m – `square` = 9n – `square`
∴ `square` = 2n
∴ `m/n = square`
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 ______.
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.
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 I ask you to construct ΔPQR ~ ΔABC exactly (when we say exactly, we mean the exact relative positions of the triangles) as given in the figure, (Assuming I give you the dimensions of ΔABC and the Scale Factor for ΔPQR) what additional information would you ask for?
If the perpendicular distance between AP is given, which vertices of the similar triangle would you find first?
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?
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. |
To construct a triangle similar to a given ∆ABC with its sides `7/3` of the corresponding sides of ∆ABC, draw a ray BX making acute angle with BC and X lies on the opposite side of A with respect to BC. The points B1, B2, ...., B7 are located at equal distances on BX, B3 is joined to C and then a line segment B6C' is drawn parallel to B3C where C' lies on BC produced. Finally, line segment A'C' is drawn parallel to AC.
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.
