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Introduction to Construction

Can a triangl...

Question

Can a triangle have
(i) two right angles?
(ii) all angles equal to 60°?
(iii) two acute angles?
Justify your statement in each case.

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Can a triangle have:

(i) Two right angles?

(ii) Two obtuse angles?

(iii) Two acute angles?

(iv) All angles more than $60^{\circ}$ ?

(v) All angles less than $60^{\circ} ?$

(vi) All angles equal to $60^{\circ} ?$

Justify your answer in each case.

Q. Can a triangle have:

(i) Two right angles?

(ii) Two obtuse angles?

(iii) Two acute angles?

(iv) All angles more than 60°?

(v) All angles less than 60°?

(vi) All angles equal to 60°?

Q. Can a triangle have
(i) two right angles?
(ii) two obtuse angles?
(iii) two acute angles?
(iv) each angle more than 60°?
(v) each angle less than 60°?
(vi) each angle equal to 60°?

Q. State 'True' or 'False':
(i) A triangle can have two right angles.
(ii) A triangle cannot have two obtuse angles.
(iii) A triangle cannot have two acute angles.
(iv) A triangle can have each angle less than 60°.
(v) A triangle can have each angle equal to 60°.
(vi) There cannot be a triangle whose angles measure 10°, 80° and 100°.

Q. Is it possible to have a triangle, in which
(i) two of the angles are right?
(ii) two of the angles are obtuse?
(iii) two of the angles are acute?
(iv) each angle is less than 60°?
(v) each angle is greater than 60°?
(vi) each angle is equal to 60°?
Give reasons in support of your answer in each case.

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