Lines, Angles And Triangle: Download Mathematics Study Notes Free PDF For REET Exam_00.1
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Lines, Angles And Triangle: Download Mathematics Study Notes Free PDF For REET Exam

Lines, Angles And Triangle: Download Mathematics Study Notes Free PDF For REET Exam_40.1

Mathematics is an equally important section for  REETMPTET & DSSSB Exams and has even more abundant importance in some other exams conducted by central or state govt. Generally, there are questions asked related to basic concepts and properties of the Geometry.

To let you make the most of Mathematics section, we are providing important facts related to the Geometry.At least 2-3 questions are asked from geometry topic in most of the teaching exams. We wish you all the best of luck to come over the fear of the Mathematics section.

How to Overcome Exam Fever, Especially When You Fear Maths

Geometry

Polygon: Two types of angle

  1. Exterior
  2. Interior
  1. Exterior Angle: Sum of exterior Angle of the polygon is 360°,

Lines, Angles And Triangle: Download Mathematics Study Notes Free PDF For REET Exam_50.1Interior Angle: Sum of the interior angle of the polygon is (n – 2)× 180.

Lines, Angles And Triangle: Download Mathematics Study Notes Free PDF For REET Exam_60.1

  1. Vertical opposite angle always be same

Lines, Angles And Triangle: Download Mathematics Study Notes Free PDF For REET Exam_70.1

-: ∠ 1 = ∠ 3  and ∠ 1 + ∠ 2= 180°

-: ∠ 2 = ∠ 4  and   ∠ 3 + ∠ 4 = 180°

Mathematics Study Notes For All Teaching Exams

  1. Corresponding angles:

∠ 4 + ∠ 5 = 180°

∠ 3 + ∠ 6 = 180°

Lines, Angles And Triangle: Download Mathematics Study Notes Free PDF For REET Exam_80.1

  1. Sum of 2 interior angle opposite to exterior angle

Lines, Angles And Triangle: Download Mathematics Study Notes Free PDF For REET Exam_90.1

5. In the given fig. AB = AC, then AD which is median of the triangle also be height of triangle

Lines, Angles And Triangle: Download Mathematics Study Notes Free PDF For REET Exam_100.1

  • In the given fig. ABCD is a cyclic quadrilateral.

Lines, Angles And Triangle: Download Mathematics Study Notes Free PDF For REET Exam_110.1

∠ A + ∠ C = 180°  (opp. Angle)

∠ B + ∠ D = 180°

⟹ opposite interior angle is equal to exterior angle.

Get free Study material for REET Exam

  • Centres of the triangle:

Type of centres:

  • Centroid
  • Incentre
  • Circum-centre
  • Ortho – centre

(1) Centroid: Intersecting points of the medians of triangle is known as centroid of the triangle.

Lines, Angles And Triangle: Download Mathematics Study Notes Free PDF For REET Exam_120.1

Area of ∆ ABD = ∆ ACD

AG : GD = 2 : 1

Area of ∆ BGC = ∆ AGC = ∆ AGB

Area of ∆ nzGY : ∆ ABC

2 : 36

1 : 18

Example: PS is the median of a triangle PQR and O is centroid such that PS = 27 cm. The length of PO is

Sol. PS is the median and O is the centroid —– (given)

PS = 27 cm

Ratio of PO : OS

Practice REET Subject wise Quiz

(2) Incentre:  Intersecting points of angle bisector of triangle is known as Incentre of the triangle

Lines, Angles And Triangle: Download Mathematics Study Notes Free PDF For REET Exam_130.1

Ix = Iy = Iz = radius

Lines, Angles And Triangle: Download Mathematics Study Notes Free PDF For REET Exam_140.1

Example: O is the incentre of triangle PQR, ∠ PQR = 70° and ∠PRQ = 60°, Then find the value of ∠ QOR.

Sol. Acc. to Question

Lines, Angles And Triangle: Download Mathematics Study Notes Free PDF For REET Exam_150.1

QO and RO are the angle bisector

∴ ∠ RQO = 35° and ∠ QRO = 30°

In ∆ QOR, ∠ RQO + ∠ QRO + ∠ QOR = 180°

35° + 30° + ∠ QOR = 180°

∠ QOR = 180° – 65° ⟹ 115°

(3) Circum-centre: Intersecting point of the perpendicular bisector of triangle is known as circum-centre of the triangle

Lines, Angles And Triangle: Download Mathematics Study Notes Free PDF For REET Exam_160.1

AO = OB = OC = Radius

∠BOC = 2 (∠BAC)

In right ∠ ∆ circum-centre is formed on the mid-point of hypotenuse.

Lines, Angles And Triangle: Download Mathematics Study Notes Free PDF For REET Exam_170.1

Lines, Angles And Triangle: Download Mathematics Study Notes Free PDF For REET Exam_180.1

(4) Ortho-centre: intersecting points of the altitudes of triangle is known as orthocentre of the triangle

Lines, Angles And Triangle: Download Mathematics Study Notes Free PDF For REET Exam_190.1

Example:  In an obtuse angled triangle ABC, ∠B is obtuse angled and O is orthocentre. ∠ AOC = 69° and ∠ ABC is

Sol. ∠ ABC = 180° – ∠ AOC

= 180° – 69°

= 111°

Some important facts of the triangle:

  1. Mid-Point Theorem: In triangle ABC, P and Q are mid – point of AB and AC. Then PQ always || to BC (PQ || BC).

Lines, Angles And Triangle: Download Mathematics Study Notes Free PDF For REET Exam_200.1

  1. Median theorem: In ∆ ABC, AD is Median

Lines, Angles And Triangle: Download Mathematics Study Notes Free PDF For REET Exam_210.1

Example: If the length of the three sides of a triangle is a 9 cm, 40 cm, and 41 cm then find the length of median to its greatest side.

Sol. This is a right-angled triangle

Lines, Angles And Triangle: Download Mathematics Study Notes Free PDF For REET Exam_220.1

  • Angle bisector theorem: Internal angle bisector

Lines, Angles And Triangle: Download Mathematics Study Notes Free PDF For REET Exam_230.1

External angle bisector:

Lines, Angles And Triangle: Download Mathematics Study Notes Free PDF For REET Exam_240.1

  • In the right Triangle ABC, F and D is the mid – points of AB and BC

Lines, Angles And Triangle: Download Mathematics Study Notes Free PDF For REET Exam_250.1

Download Geometry Study Notes PDF (English)

Download Geometry Study Notes PDF (Hindi)

 

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