ALTERNATE EXTERIOR ANGLES
Definition Of Alternate Exterior Angles
When two lines are cut by another line (transversal), the pairs of angles formed outside the two lines and on the opposite of the transversal are called Alternate Exterior Angles.
More about Alternate Exterior Angles
If two parallel lines are cut by a transversal, the alternate exterior angles are congruent.
Examples of Alternate Exterior Angles
AB || CD and EF is the transversal cutting the parallel lines. So, ∠2 and ∠8, ∠1 and ∠7 are the pairs of alternate exterior angles in the figure shown.
Video Examples: Alternate Exterior Angles
Solved Example on Alternate Exterior Angles
Ques:
PQ and RS are two lines and UT is a transversal of PQ and RS. Which among the following is a pair of alternate exterior angles?
Choices:
A. ∠4 and ∠5
B. ∠2 and ∠8
C. ∠1 and ∠2
D. ∠1 and ∠8
Correct Answer: D
Solution:
Step 1: When two lines are cut by another line (transversal), the pairs of angles formed outside the two lines and on the opposite of the transversal are called Alternate Exterior Angles.
Step 2: From the figure, PQ and RS are parallel lines and UT is a transversal passing through the parallel lines.
Step 3: The pairs of alternate exterior angles are
∠1 and ∠8
∠2 and ∠7
Step 4: Hence, ∠1 and ∠8 are the alternate exterior angles in the given figure.
Quick Summary
- Alternate exterior angles are formed outside two lines cut by a transversal.
- If the two lines are parallel, the alternate exterior angles are congruent.
⚠️ Common Mistakes
- Confusing alternate exterior angles with alternate interior angles.
- Assuming alternate exterior angles are always congruent, even when the lines are not parallel.
🌍 Real-World Uses
- Architects using parallel lines in building design and ensuring that angles of support beams on opposite sides of a structure are equal for stability.
- Carpenters cutting crown molding where alternate exterior angles need to be equal to ensure a consistent and aesthetically pleasing finish.
- Surveyors using transits to measure angles and determine land boundaries, relying on alternate exterior angles for accurate calculations across parallel property lines.
📋 Standards Alignment
CCSS.MATH.CONTENT.8.G.A.5
🔗 Related Links
🍎 Teacher Insights
Use visual aids and real-world examples to help students understand the concept of alternate exterior angles. Emphasize the importance of parallel lines for the congruence of these angles.🎓 Prerequisites
- Understanding of angles
- Knowledge of parallel lines
- Understanding of transversals
Check Your Knowledge
Q1: Which of the following pairs of angles are alternate exterior angles?
Q2: If two parallel lines are cut by a transversal and one alternate exterior angle is 60 degrees, what is the measure of the other alternate exterior angle?
Frequently Asked Questions
Q: Are alternate exterior angles always equal?
A: No, alternate exterior angles are only equal when the two lines intersected by the transversal are parallel.
Q: What is a transversal?
A: A transversal is a line that intersects two or more other lines at distinct points.