Answer:
- a||b--------Given
- ∠1≅∠2-------definition of corresponding angles
- m∠1=m∠2------corresponding angles are congruent
- ∠2 and ∠3 are supplementary-------definition of linear pair
- m∠2+m∠3=180°-------If two angles form a linear pair, their angle measures to 180°
- m∠1+m∠3=180°---------proved earlier m∠1=m∠2
Step-by-step explanation:
In geometry, transversal is a line which cuts 2 or more lines, often parallel lines.
When lines are cut by a transversal,
- angles which occupy same relative position are termed as corresponding angles. If the lines are parallel then corresponding angles are congruent.
- pairs of angles on either side of transversal are termed as alternate interior angles. If the lines are parallel then alternate interior angles are congruent.
- If lines are parallel, then pairs of consecutive interior angles formed are supplementary
It is given that, a||b
By the definition of corresponding angles,
∠1≅∠2
⇒m∠1=m∠2(as corresponding angles are congruent when parallel lines are cut by a transversal)
∠2 and ∠3 are supplementary, as they form a linear pair
⇒m∠2+m∠3=180°(If two angles form a linear pair, their angle measures sum to 180°)
⇒m∠1+m∠3=180° (m∠1=m∠2 as we have proved above)
