How many triangles $(△ A B C)$ can be constructed if a side $(A B)$ and the angle opposite to the side $(A B)$ are given?

No triangle, a triangle cannot be formed with one line and one angle.

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Two different triangles, one above the given line and one below.

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Infinitely many, as the other two sides are not given.

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Unique triangle, the side opposite the angle is also given.

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Solution

The correct option is C Infinitely many, as the other two sides are not given.

If we construct a triangle:

1.Draw a ray $B C$ of any length.

2.With C as the center, draw an angle $∠ B C A$ of the given dimensions.

3.As the length of $A B$ is given, with the given length as the radius and any point on $B C$ , mark an arc on $A C$ .

4.By joining the point on $A B$ and the point on $A C$ , form a triangle.

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Similar questions

Fill in the blanks in the following so that each of the following statements is true.

(i) Sides opposite to equal angles of a triangle are ___

(ii) Angle opposite to equal sides of a triangle are ___

(iii) In an equilateral triangle all angles are ___

(iv) In a $Δ A B C i f ∠ A = ∠ C, t h e n A B =$ ___

(v) If altitudes CE and BF of a triangle ABC are equal, then AB = ___

(vi) In an isosceles, triangle ABC with AB = AC, if BD and CE are its altitudes then BD is ___ CE.

(vii) In right triangles ABC and DEF, if hypotenuse AB = EF and side AC = DE, then $Δ A B C ≅ Δ$ ___

Q. Fill in the blanks in the following so that each of the following statements is true.

(i) Sides opposite to equal angles of a triangle are .......

(ii) Angle opposite to equal sides of a triangle are .......

(iii) In an equilateral triangle all angles are ........

(iv) In a ABC if ∠A = ∠C, then AB = ............

(v) If altitudes CE and BF of a triangle ABC are equal, then AB = ........

(vi) In an isosceles triangle ABC with AB = AC, if BD and CE are its altitudes, then BD is ...... CE.

(vii) In right triangles ABC and DEF, if hypotenuse AB = EF and side AC = DE, then ΔABC ≅ Δ .........

Draw a triangle ABC with side BC = 6 cm, AB = 5 cm and ∠ABC = 60°. Then construct a triangle whose sides areof the corresponding sides of the triangle ABC.

Give the justification of the construction.

Q. ABC is an isosceles triangle, right-angled at B. similar triangles ACD and ABE are constructed on sides AC and AB. Find the ratio between the areas of ∆ABE and ∆ACD.

Draw a triangle $A B C$ with side $B C = 6 c m$ , $A B = 5 c m$ and $∠ A B C = 60^{\circ}$ , Then construct a triangle whose sides are $\frac{3}{4}$ of the corresponding sides of the triangle $A B C$ .

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How many triangles (△ABC) can be constructed if a side (AB) and the angle opposite to the side (AB) are given?

How many triangles $(△ A B C)$ can be constructed if a side $(A B)$ and the angle opposite to the side $(A B)$ are given?