Straight Lines
Angle Bisectors
Grade 11
Question:
<p>Find the third side of a configuration given that it is parallel to the angle bisectors of two given lines.</p>
<p>(a) Parallel to first angle bisector</p>
<p>(b) Parallel to second angle bisector</p>
<p>(c) Perpendicular to the angle bisectors</p>
<p>(d) Other orientation</p>
Step-by-Step Solution
Key Concept: Understand the relationship between angle bisectors and use properties of parallel and perpendicular lines.
<p><strong>Step 1:</strong> The third side is parallel to the angle bisectors of the given two lines.</p><p><strong>Step 2:</strong> The angle bisectors of two lines are perpendicular to each other.</p><p><strong>Step 3:</strong> Therefore, the third side can be parallel to either the first or second angle bisector.</p><p><strong>Step 4:</strong> It is also perpendicular to the other angle bisector.</p><p>∴ Answer is (a, c).</p>
Correct Answer: a, c