1- In the diagram, all b. Identify whether each pair of angles are corresponding angles alternate interior, alternate exterior, same-side interior, same-side exterior. T. 27 and 21 6. 24 and 25 a 2.22 and 26 7.25 and 23 5/8 3. 26 and 24 8. 28 and 24 3 6/7 4.2 and 28 9.27 and 22 5.
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Transversal
In geometry, a transversal is a line that intersects two or more other (often parallel ) lines.
In the figure below, line n is a transversal cutting lines l and m .
When two or more lines are cut by a transversal, the angles which occupy the same relative position are called corresponding angles .
In the figure the pairs of corresponding angles are:
∠1 and ∠5∠2 and ∠6∠3 and ∠7∠4 and ∠8
When the lines are parallel, the corresponding angles are congruent .
When two lines are cut by a transversal, the pairs of angles on one side of the transversal and inside the two lines are called the consecutive interior angles .
In the above figure, the consecutive interior angles are:
∠3 and ∠6∠4 and ∠5
If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles formed are supplementary .
When two lines are cut by a transversal, the pairs of angles on either side of the transversal and inside the two lines are called the alternate interior angles .
In the above figure, the alternate interior angles are:
∠3 and ∠5∠4 and ∠6
If two parallel lines are cut by a transversal, then the alternate interior angles formed are congruent .
When two lines are cut by a transversal, the pairs of angles on either side of the transversal and outside the two lines are called the alternate exterior angles .
In the above figure, the alternate exterior angles are:
∠2 and ∠8∠1 and ∠7
If two parallel lines are cut by a transversal, then the alternate exterior angles formed are congruent .
Example 1:
In the above diagram, the lines j and k are cut by the transversal l . The angles ∠c and ∠e are…
A. Corresponding Angles
B. Consecutive Interior Angles
C. Alternate Interior Angles
D. Alternate Exterior Angles
The angles ∠c and ∠e lie on either side of the transversal l and inside the two lines j and k .
Therefore, they are alternate interior angles.
The correct choice is C .
Example 2:
In the above figure if lines AB←→ and CD←→ are parallel and m∠AXF=140° then what is the measure of ∠CYE ?
The angles ∠AXF and ∠CYE lie on one side of the transversal EF←→ and inside the two lines AB←→ and CD←→ . So, they are consecutive interior angles.
Since the lines AB←→ and CD←→ are parallel, by the consecutive interior angles theorem , ∠AXF and ∠CYE are supplementary.
That is, m∠AXF+m∠CYE=180° .
But, m∠AXF=140° .
Substitute and solve.
140°+m∠CYE=180°140°+m∠CYE−140°=180°−140°m∠CYE=40°