Rational and Irrational Numbers
Parallel Lines and Transversal
- Pairs of Lines - Transversal
- Pairs of Lines - Angles Made by a Transversal
- Pairs of Lines - Transversal of Parallel Lines
- Properties of Angles Formed by Two Parallel Lines and a Transversal
- Axiom: If a Transversal Intersects Two Parallel Lines, Then Each Pair of Corresponding Angles is Equal.
- Axiom: If a Transversal Intersects Two Parallel Lines, Then Each Pair of Alternate Interior Angles Are Equal.
- Axiom: If a Transversal Intersects Two Parallel Lines, Then Each Pair of Interior Angles on the Same Side of the Transversal is Supplementary.
- To Draw a Line Parallel to the Given Line Through a Point Outside the Given Line Using Set-square.
- To Draw a Parallel Line to a Given Line at a Given Distance.
Indices and Cube Root
- Concept of Exponents
- Multiplying Powers with the Same Base
- Dividing Powers with the Same Base
- Taking Power of a Power
- Multiplying Powers with Different Base and Same Exponents
- Dividing Powers with Different Base and Same Exponents
- Numbers with Exponent Zero, One, Negative Exponents
- Meaning of Numbers with Rational Indices
- Concept of Cube Number
- Concept of Cube Root
- Cube Root Through Prime Factorisation Method
Altitudes and Medians of a Triangle
Factorisation of Algebraic Expressions
Quadrilateral : Constructions and Types
Discount and Commission
Division of Polynomials
Equations in One Variable
Congruence of Triangles
Surface Area and Volume
Circle - Chord and Arc
Constructing an Altitude of a Triangle:
I. Constructing an Altitude for an Acute Triangle:
- Draw an Acute angle Triangle ΔXYZ.
- Draw a perpendicular from vertex X on the side YZ using a set-square. Name the point where it meets side YZ as R. Seg XR is an altitude on
- Considering side XZ as a base, draw an altitude YQ on side XZ. seg YQ ⊥ seg XZ.
- Consider side XY as a base, draw an altitude ZP on seg XY. seg ZP ⊥ seg XY.
seg XR, seg YQ, seg ZP are the altitudes of ΔXYZ.
- Note that, the three altitudes are concurrent. The point of concurrence is called the orthocentre of the triangle. It is denoted by the letter ‘O’.
II. Constructing an Altitude for an Obtuse Triangle:
- Draw an obtuse triangle. Label it ΔABC, Extend side `bar(AC)`, beyond point A.
- Construct a perpendicular line to `bar(AC)`, through B.
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