Question

Prove that the angles A is equal to Angle C ... Using the alternate angle theorom
The question is in Cambridge Checkpoint Mathematics Practice Book 8 page 30.

Answer 1

Answer:

Axiom 3: If a transversal intersects two parallel lines, then each pair of corresponding angles is equal.

lines & angles 3

Here, Exterior angles are ∠1, ∠2, ∠7 and ∠8

Interior angles are ∠3, ∠4, ∠5 and ∠6

Corresponding angles are ∠

(i) ∠1 and ∠5

(ii) ∠2 and ∠6

(iii) ∠4 and ∠8

(iv) ∠3 and ∠7

Axiom 4 If a transversal intersects two lines such that a pair of corresponding angles is equal, then the two lines are parallel to each other.

Thus, (i) ∠1 = ∠5, (ii) ∠2 = ∠6, (iii) ∠4 = ∠8 and (iv) ∠3 = ∠7

Alternate Interior Angles: (i) ∠4 and ∠6 and (ii) ∠3 and ∠5

Alternate Exterior Angles: (i) ∠1 and ∠7 and (ii) ∠2 and ∠8

If a transversal intersects two parallel lines then each pair of alternate interior and exterior angles are equal.

Alternate Interior Angles: (i) ∠4 = ∠6 and (ii) ∠3 = ∠5

Alternate Exterior Angles: (i) ∠1 = ∠7 and (ii) ∠2 = ∠8

Interior angles on the same side of the transversal line are called the consecutive interior angles or allied angles or co-interior angles. They are as follows: (i) ∠4 and ∠5, and (ii) ∠3 and ∠6

Answer 2

Answer:

Refer to the attachment