Which lines are parallel? justify your answer.

a) lines a and b are parallel because their corresponding angles are congruent.
b) lines a and b are parallel because their same side exterior angles are congruent.
c) lines e and f are parallel because their corresponding angles are congruent.
d) lines e and f are parallel because their same side exterior angles are supplementary.

The is correct match.

Further explanation:

If two parallel lines intersected by a third line called as a transversal line, it froms eight angles as shown in Figure 1.

The eight angles will together form four pairs of corresponding angles.

and constitutes one of the pairs. Corresponding angles are congruent. All angles that have the same position with regards to the parallel lines and the transversal are corresponding pairs.e.g. , , .

Angles that are in the area between the parallel lines like and above are called interior angles whereas the angles that are on the outside of the two parallel lines like and are called exterior angles.

Angles that are on the opposite sides of the transversal are called alternate angles.e.g. .

All the angles that are either exterior pair of angles, interior pair of angles, alternate pair of angles or corresponding pair of angles are all congruent.

From the figure 2, it is observed that for line e and f the sum of same side exterior angle is not 180 that is 110+80=190. Therefore, for line e and f the corresponding angle are not congruent.

In line a and b corresponding angles are congruent that is 110.Therefore line a and b are parallel to each others.

Thus, the is correct.  

Learn more:  

1. Which rule describes the transformation? link  

2. Which undefined term is needed to define an angle? link  

3. Look at the figure, which trigonometric ratio should you use to find x? link  

Answer Details:  

Grade: Senior School  

Subject: Mathematics  

Chapter: Coordinate geometry.  

Keywords:

Angle ,interior angle, exterior angles, alternate angles, corresponding angles, transversal lines, parallel lines, triangle, similar triangle, ratio of sides, equal angles, square of hypotenuse, sum, square of legs, sum of square of legs, sum of angle of triangle, property of triangle, angle A,  angle B, angle C.

- 2 + 10x³ - 21x² + 19x - 4

step-by-step explanation:

each term in the second factor is multiplied by each term in the first factor

x²(- 2x² + 4x - 1) - 3x(- 2x² + 4x - 1) + 4(- 2x² + 4x - 1) ← distribute

= - 2 + 4x³ - x² + 6x³ - 12x² + 3x -8x² + 16x - 4

collect like terms

= - 2 + 10x³ - 21x² + 19x - 4 ← in standard form