#### Topics

##### 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

##### Expansion Formulae

##### Factorisation of Algebraic Expressions

##### Variation

##### Quadrilateral : Constructions and Types

##### Discount and Commission

##### Division of Polynomials

##### Statistics

##### Equations in One Variable

##### Congruence of Triangles

##### Compound Interest

##### Area

##### Surface Area and Volume

##### Circle - Chord and Arc

#### theorem

**If a transversal intersects two parallel lines, then each pair of corresponding angles is equal.**

This is also referred to as the **corresponding angles axiom**.

**Given:** Two Parallel lines PQ and RS.

Let AB be the transversal intersecting PQ at M and RS and N.

**To Prove: **Each pair of corresponding angles are equal.

i.e., ∠ AMP ≅ ∠ MNR, ∠ PMN ≅ ∠ RNB,

and ∠ AMQ ≅ ∠ MNS, ∠ QMN ≅ ∠ SNB.

**Proof: **

First, we will prove ∠ AMP ≅ ∠ MNR.

For lines PQ and RS with transversal AB,

∠QMN = ∠MNR ......(Alternate Interior angles)(1)

For lines PQ and AB,

∠AMP = ∠QMN .......(Vertically opposite angles)(2)

From (1) and (2),

∠AMP = ∠MNR

Similarly, we can prove that

∠ PMN ≅ ∠ RNB,

∠ AMQ ≅ ∠ MNS,

∠ QMN ≅ ∠ SNB.

Hence, Each pair of corresponding angles are equal.

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