Advertisements
Advertisements
प्रश्न
ΔAMT ~ ΔAHE. In ΔAMT, AM = 6.3 cm, ∠MAT = 120°, AT = 4.9 cm, `(AM)/(HA) = 7/5`, then construct ΔAMT and ΔAHE.
Advertisements
उत्तर
Steps of construction:
- Draw seg AT of length 4.9 cm.
- Take ∠A as 120° and draw an arc of 6.3 cm on it. Name the point as M.
- Join seg MT to obtain ΔAMT.
- Draw ray AB such that ∠TAB is an acute angle.
- Locate points B1, B2, B3, B4, B5, B6, B7 on ray AB such that, AB1 = B1B2 = B2B3 = B3B4 = B4B5 = B5B6 = B6B7.
- Join point T and B7.
- Through point B5 draw a line parallel to seg TB7 which intersects seg AT at point E.
- Draw a line parallel to MT through E to intersect line AM at point H.
∆AHE is the required triangle similar to ∆AMT.
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.
Find the ratio in which the line segment joining the points A(3,- 3) and B(- 2, 7) is divided by x-axis. Also find the coordinates of the point of division.
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 line segment of length 8 cm and divide it internally in the ratio 4 : 5.
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.
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.
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 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.
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.
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`.
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.
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 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.
The line segment AB is divided into five congruent parts at P, Q, R and S such that A–P–Q–R–S–B. If point Q(12, 14) and S(4, 18) are given find the coordinates of A, P, R, B.
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 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.
In the figure ΔABC ~ ΔADE then the ratio of their corresponding sides is:
∆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.
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 ______.
When a line segment is divided in the ratio 2 : 3, how many parts is it divided into?
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?
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.
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.
By geometrical construction, it is possible to divide a line segment in the ratio `sqrt(3) : 1/sqrt(3)`.
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 line segment of length 7 cm. Find a point P on it which divides it in the ratio 3:5.
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`.
