In which of the following situations an angle bisector cannot be constructed to bisect the angle formed between two given lines?

Two intersecting lines

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Two parallel lines

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Two perpendicular lines

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None of the above

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Solution

The correct option is B Two parallel lines
Since two parallel lines do not intersect each other, an angle cannot be formed between them. Thus in this case, angle bisection is not possible.

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Q. In which of the following situations an angle bisector cannot be constructed to bisect the angle formed between two given lines?

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Q. To construct a triangle ABC in which

∠ B = 60^{\circ}, ∠ C = 45^{\circ}

and AB + BC + AC = 12 cm

The steps of construction are:
Step 1: Draw a line segment XY=12 cm
Step 2: At X, construct an angle of $60^{\circ}$ and at y construct an angle of $45^{\circ}$
Step 3: Bisect these angles. Let bisector of these angles intersect at point A
Step 4 will be

Complete the steps to construct a triangle XYZ in which $∠ Y = 45^{\circ}, ∠ Z = 90^{\circ}$ and XY + YZ + ZX = 13 cm.

Steps of construction:
Step 1: Draw a line segment AB=13 cm
Step 2: At A, Construct an angle of $45^{\circ}$ and at B construct an angle of $90^{\circ}$
Step 3 will be

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In which of the following situations an angle bisector cannot be constructed to bisect the angle formed between two given lines?

The correct option is B Two parallel linesSince two parallel lines do not intersect each other, an angle cannot be formed between them. Thus in this case, angle bisection is not possible.

The correct option is B Two parallel lines
Since two parallel lines do not intersect each other, an angle cannot be formed between them. Thus in this case, angle bisection is not possible.