In ∆POR, bisector of angle Q intersects PR in S. If 2PS=3R and PQ=6.3 then find QR
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Step-by-step explanation:
Mathematics NCERT Grade 9, Chapter 6: Lines and Angles: In this chapter students will study the properties of the angle formed when two lines intersect each other and properties of the angle formed when a line intersects two or more parallel lines at distinct points. The chapter starts from zero level, the first topic of the chapter being Basic Terms and Definitions.
Acute angle: Measures between 0° and 90°.
Right angle: Exactly equal to 90°.
Obtuse angle: Angle greater than 90° but less than 360°.
Reflex angle: Angle greater than 180° but less than 360°.
Two angles whose sum is 90° are called complementary angles.
Two angles whose sum is 180° are called supplementary angles.
Adjacent angles, linear pair of angles and vertically opposite angles are other important topics in this chapter.
Section 6.3 is about the topic- Intersecting Lines and Non-Intersecting Lines.
If two lines intersect each other, then the vertically opposite angles are equal.
After that, the topic- Pair of Angles is discussed. 2 axioms, 1 theorem, and some solved examples are also given in this section.
Axiom 6.1 states about linear pair of angles.
Linear pair axiom is discussed.
Exercise 6.1 contains various questions based on all the concepts discussed in the section.
The next section is about Parallel Lines and a Transversal. Axioms and theorems about this concept are explained.
Lines that are parallel to a given line are parallel to each other.
Corresponding angles axiom is also discussed.
Theorem on alternate interior angles is also given in this chapter.
Moving on, students will find a detailed description of Lines parallel to the Same Line. Exercise 6.2 contains 6 questions.
Lines parallel to the same line is discussed with the help of corresponding angles axiom.
Then chapter will also lay emphasis on Angle Sum Property.
The sum of the three angles of a triangle is 180°.
Exterior angle of a triangle is greater than the sum of the interior opposite angles.
Theorem and examples are given in this section. After that, another unsolved exercise i.e 6.3 is given.
In the end, a summary of the chapter is provided.