AB and PQ are parallel lines. CR and DS intersect the two lines as shown in the figure. Which statement is true about CR and DS?
2 answers:
Answer with explanation:
It is given that, AB and P Q are parallel lines.Line segment CR and D S, intersect the two lines.
Line segment CR and D S ,are Transversal to parallel lines, AB and P Q.
⇒∠C + ∠ R=180°
⇒90°+∠ R=180°
∠ R=180°-90°
∠R=90°
Similarly, ∠S=90°
→∠R+∠S=90°+90°=180°
As, sum of interior angles on the same side of transversal is 180°, so lines are Parallel.
→CR║DS
Also, AB║CD→CD║RS.
If in a Quadrilateral, opposite sides are parallel, then it is a Parallelogram,and also each interior angle has measure 90°, so it is a Rectangle.
In a rectangle opposite sides are equal.
Option C: →CR =D S
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