Question

In the figure AB and CD are intersected by a transversal at P and Q .Is line AB parallel to CD. Justify

Answer 1

Answer:

proved

Step-by-step explanation:

ray PR ∥ SQ and PQ is transversal (given)

To find: AB ∥ CD

∠ RPQ ≅ ∠ PQS (alternate angle) two angle formed when a line crosses two other lines, that lie on opposite side of the transversal line and on opposite relative sides of the other lines. If the two lines crossed are parallel, the alternate angles are equal.)

X = y

∠ BPQ = 2x (ray PR bisect ∠ BPQ)

∠ PQC = 2y (ray SQ bisect ∠ PQC)

When a line, shape, or angle inti two exactly equal parts is called bisector.

X = y

2x = 2y (multiply 2 on both side)

∠ BPQ = ∠ PQC

But they form a pair of alternate angle that are congruent.

∴ AB ∥ CD (hence proved)

hope you like my answer

Answer 2

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HERE IS UR ANSWER

$_____________________________$

Line AB||CD

$\fbox{♧Corresponding angles are equal♧}$

$\angle \: 1 = \angle2 \\ \angle3 = \angle4 \\ \angle5 = \angle7 \\\angle6 = \angle8$

$\fbox{♧Alternate angles are equal♧}$

$\angle5 = \angle4 \\ \angle1 =\angle8 \\ \angle6 = \angle2 \\ \angle3 = \angle7$

$\fbox{♧Sum of two co-interior angles is 180°♧}$

$\angle3 + \angle2 = 180 \degree \\ \angle6 + \angle7 = 180 \degree$