Advertisements
Advertisements
Question
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.
Solution
Given:
BC = 6 cm, ∠C = 30° and ∠A = 105°
∴∠B = 180° − (∠A + ∠C) (In ΔABC, ∠A + ∠B + ∠C = 180°)
= 180° − (105° + 30°)
= 45°
Steps of construction:
1. Draw a line BC = 6 cm.
2. Draw a ray CN making an angle of 30° at C.
3. Draw a ray BM making an angle of 45° at B.
4. Locate the point of intersection of rays CN and BM and name it as A.
5. ABC is the triangle whose similar triangle is to be drawn.
6. Draw any ray BX making an acute angle with BC on the side opposite to the vertex A.
7. Locate 3 (Greater of 2 and 3 in`2/3`) points B1, B2 and B3 on BX so that BB1 = B1B2 = B2B3 .
8. Join B3C and draw a line through B2 (Smaller of 2 and 3 in `2/3`) parallel to B3C to intersect BC at C’.
9. Draw a line through C’parallel to the line CA to intersect BA at A’.
10. A’BC’ is the required similar triangle whose sides are `2/3` times the corresponding sides of ΔABC.
APPEARS IN
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 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.
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.
Given A(4, –3), B(8, 5). Find the coordinates of the point that divides segment AB in the ratio 3 : 1.
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 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.
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 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?
The point W divides the line XY in the ratio m : n. Then, the ratio of lengths of the line segments XY : WX is ______.
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.
