Q25 of 115 Page 8

In Fig 8.121, arms BA and BC of ∠ABC are respectively parallel to arms ED and EF of ∠DEF. Prove that ∠ABC + ∠DEF = 180°

Given that,

AB ‖ DE and BC ‖ EF


To prove: ∠ABC + ∠DEF = 180o


Construction: Produce BC to intersect DE at M


Proof: Since, AB ‖ EM and BL is the transversal


∠ABC = ∠EML (Corresponding angles) (i)


Also,


EF ‖ ML and EM is the transversal


By the property co interior angles are supplementary


∠DEF + ∠EML = 180o(ii)


From (i) and (ii), we have


∠DEF + ∠ABC = 180o


Hence, proved


More from this chapter

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23

If, l, m, n are three lines such that l||m and n⊥ l, prove that n⊥ m.

 24

In Fig 8.120, arms BA and BC of ∠ABC are respectively parallel to arms ED and EF of ∠DEF. Prove that ∠ABC = ∠DEF.

 26

Which of the following statements are true (T) and which are false (F)? Give reasons.

(i) If two lines are intersected by a transversal, then corresponding angles are equal.


(ii) If two parallel lines are intersected by a transversal, then alternate interior angles are equal.


(iii) Two lines perpendicular to the same line are perpendicular to each other.


(iv) Two lines parallel to the same line are parallel to each other.


(v) If two parallel lines are intersected by a transversal, then the interior angles on the same side of the transversal are equal.

 27

Fill in the blanks in each of the following to make the statement true:

(i) If two parallel lines are intersected by a transversal, then each pair of corresponding angles are …..


(ii) If two parallel lines are intersected by a transversal, then interior angles on the same side of the transversal are ……….


(iii) Two lines perpendicular to the same line are …….. to each other.


(iv) Two lines parallel to the same line are ….. to each other.


(v) If a transversal intersects a pair of lines in such away that a pair of alternate angles are equal, then the lines are …………


(vi) If a transversal intersects a pair of lines in such away that the sum of interior angles on the same side of transversal is 180°, then the lines are ……