Find whether each of the following triangle can be constructed with the given information or not?
$∠ A = 90 °, ∠ C = 45 °, B C = 4 c m$

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Solution

$∠ A + ∠ B + ∠ C = 180 ° . . . (b y a n g l e s u m p r o p e r t y) 90 ° + ∠ B + 45 ° = 180 ° ∠ B + 135 ° = 180 ∠ B = 180 ° - 135 ° ∠ B = 45 °$
Now we have two angles $∠ B, ∠ C$ and their included side $B C$ is given so triangle can be constructed.

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Question 21
In which of the following cases, a unique triangle can be drawn?
a) AB = 4 cm, BC = 8 cm and CA = 2 cm
b) BC = 5.2 cm, $∠ B = 90^{\circ} and ∠ C = 110^{\circ}$
c) XY = 5 cm, $∠ X = 45^{\circ} and ∠ Y = 60^{\circ}$
d) An isosceles triangle with the length of each equal side 6.2 cm

Find whether each of the following triangle can be constructed with the given information or not?

$∠ A = 55 °, ∠ B = 60 °, A B = 6 c m$ .

Q. A triangle ABC can be constructed in which

∠ B = 60^{o}

∠ C = 45^{o}

and AB +BC + AC = 11 cm. Is this Statement true?

Q. In which of the following, unique

△

ABC cannot be constructed with the given information? Assume AB = 5 cm for each of the options.

Write true or false for the given statement:

A triangle $A B C$ can be constructed in which $A B = 5 c m, ∠ A = 45 ° a n d B C + A C = 5 c m$ .

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Find whether each of the following triangle can be constructed with the given information or not?∠A=90°,∠C=45°,BC=4cm

∠A+∠B+∠C=180°...(byanglesumproperty)90°+∠B+45°=180°∠B+135°=180∠B=180°-135°∠B=45°Now we have two angles ∠B,∠Cand their included side BC is given so triangle can be constructed.

Find whether each of the following triangle can be constructed with the given information or not?
$∠ A = 90 °, ∠ C = 45 °, B C = 4 c m$

$∠ A + ∠ B + ∠ C = 180 ° . . . (b y a n g l e s u m p r o p e r t y) 90 ° + ∠ B + 45 ° = 180 ° ∠ B + 135 ° = 180 ∠ B = 180 ° - 135 ° ∠ B = 45 °$
Now we have two angles $∠ B, ∠ C$ and their included side $B C$ is given so triangle can be constructed.