Advertisements
Advertisements
प्रश्न
Choose the correct alternative:
In the figure ΔABC ~ ΔADE then the ratio of their corresponding sides is ______
पर्याय
`3/1`
`1/3`
`3/4`
`4/3`
Advertisements
उत्तर
`4/3`
From the given figure, we get that
AD = 3 units, DB = 1 units, and AB = 4 units ...(i)
As ∆ABC ∼ ∆ADE, we get
`"AB"/"AD" = "BC"/"DE" = "AC"/"AE"` ...[Ratio of Corresponding sides of similar triangles]
∴ `4/3 = "BC"/"DE" = "AC"/"AE"` ...[From (i)]
APPEARS IN
संबंधित प्रश्न
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.
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.
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.
Draw a triangle ABC with side BC = 7 cm, ∠B = 45°, ∠A = 105°. Then, construct a triangle whose sides are `4/3 `times the corresponding side of ΔABC. 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.
Construct a triangle similar to a given ΔABC such that each of its sides is (5/7)th of the corresponding sides of Δ ABC. It is given that AB = 5 cm, BC = 7 cm and ∠ABC = 50°.
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.
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.
Construct the circumcircle and incircle of an equilateral ∆XYZ with side 6.5 cm and centre O. Find the ratio of the radii of incircle and circumcircle.
If A(–14, –10), B(6, –2) is given, find the coordinates of the points which divide segment AB into four equal parts.
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.
Choose the correct alternative:
______ number of tangents can be drawn to a circle from the point on the circle.
Choose the correct alternative:
ΔPQR ~ ΔABC, `"PR"/"AC" = 5/7`, then
Choose the correct alternative:
∆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
ΔPQR ~ ΔABC. In ΔPQR, PQ = 3.6cm, QR = 4 cm, PR = 4.2 cm. Ratio of the corresponding sides of triangle is 3 : 4, then construct ΔPQR and ΔABC
ΔAMT ~ ΔAHE. In ΔAMT, AM = 6.3 cm, ∠MAT = 120°, AT = 4.9 cm, `"AM"/"HA" = 7/5`, then construct ΔAMT and ΔAHE
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 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 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 `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 ______.
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. |
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 ______.
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 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 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.
Two line segments AB and AC include an angle of 60° where AB = 5 cm and AC = 7 cm. Locate points P and Q on AB and AC, respectively such that AP = `3/4` AB and AQ = `1/4` AC. Join P and Q and measure the length PQ.
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 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 of length 7 cm and divide it in the ratio 5 : 3.
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]
