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Chapter Analysis
Beginner21 pages • EnglishQuick Summary
The chapter 'Parallel and Intersecting Lines' introduces students to different types of lines and angles formed when lines intersect. It covers concepts such as vertically opposite angles, linear pairs, corresponding angles, and alternate angles. The chapter also explains the conditions under which lines are parallel and introduces the concept of transversals and their properties when they intersect parallel lines.
Key Topics
- •Intersecting Lines
- •Parallel Lines
- •Vertically Opposite Angles
- •Linear Pairs
- •Corresponding Angles
- •Alternate Angles
- •Transversals
- •Conditions for Parallelism
Learning Objectives
- ✓Understand the definition of parallel and intersecting lines
- ✓Identify vertically opposite and corresponding angles
- ✓Comprehend properties of transversals with parallel lines
- ✓Learn to determine if lines are parallel based on angles
- ✓Develop skills to solve problems involving angles and lines
Questions in Chapter
In Fig. 5.33, ∠ABC = 45° and ∠IKJ = 78°. Find angles ∠GEH, ∠HEF, ∠FED.
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In Fig. 5.34, AB is parallel to CD and CD is parallel to EF. Also, EA is perpendicular to AB. If ∠BEF = 55°, find the values of x and y.
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What is the measure of angle ∠NOP in Fig. 5.35?
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Additional Practice Questions
If two intersecting lines form one angle of 30°, what are the measures of the other three angles?
easyAnswer: The other angles will be 150°, 30°, and 150°. This is because vertically opposite angles are equal and the sum of angles on a straight line is 180°.
Draw two parallel lines and a transversal. If one of the angles formed is 80°, find the measures of all eight angles.
mediumAnswer: If one angle is 80°, then its corresponding angle is also 80°. Alternate interior angles will also be 80°, and the remaining angles will be 100°, as they are linear pairs (180° - 80°).
Can three lines be both parallel and intersecting? Justify your answer.
easyAnswer: No, three lines cannot be both parallel and intersecting. If lines are parallel, they never meet; intersecting lines meet at one point.
If a transversal cuts two parallel lines, name and identify the pairs of corresponding angles.
mediumAnswer: Corresponding angles are angles in matching corners when a transversal crosses two parallel lines. For example, if lines l and m are parallel and t is the transversal, then ∠1 = ∠5, ∠2 = ∠6, ∠3 = ∠7, and ∠4 = ∠8.
Explain why alternate angles are equal when a transversal crosses two parallel lines.
mediumAnswer: Alternate angles are equal because they are formed by the transversal crossing the parallel lines and lie on opposite sides of the transversal and between the two lines.