GRE - Geometry Session 1

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Geometry Concept Session 1
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Chapter Pathway
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Triangle Properties
Polygons
Quadrilaterals
Circle Properties
Mensuration
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Building Blocks of Geometry
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Solving Linear Equations
1) Acute
2) Right
3) Obtuse
4) Reflex
Reflex
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Classification of angles
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Building blocks of Geometry
Vertically opposite
angles
Linear Pair
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Parallel lines and transversal
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Parallel lines and transversal
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Properties of Triangles
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Triangle – Basic Properties
Basic Properties
• The sum of three internal angles = 180
• The sum of three exyernal angles = 360
• Exterior angle is equal to sum of interior opposite
Side related properties
• Sum of any two sides is greater than the third side
• Difference of any two sides is lesser than the third side
• Side opposite the greater angle is greater and vice versa
• Sides opposite equal angles are equal and vice versa
Classification
• On the basis of angles
• On the basis of sides
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Problems
In the figure, find the value of 𝑥 + 𝑦 + 𝑧 (in degrees)
Answer: 143
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Congruency
- Corresponding sides and corresponding
angles are equal
- Congruency conditions
- SSS
- SAS
- AAS
- ASA
- RHS
- Properties of two congruent triangles
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Similarity
• Corresponding sides proportional;
corresponding angles are equal
• Any congruency condition is also a similarity
condition(the vice versa is not true)
• Properties of two similar triangles
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Special Triangles and their Properties
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Pythagoras theorem
Pythagoras triplets
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Special Triangles – Right Angled Triangle

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1) Special Right Angled triangles
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90-60-30
triangle
90-45-45
triangle
Side Ratios 2: √3:1 √2 : 1: 1
Special Triangles – Right Angled Triangle

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The perimeter of an isosceles right triangle is (32 + 32 2).
What is the length of the hypotenuse of the triangle?
A. 32
B. 16
C. 16 2
D.
32
2
E. 18
Problems

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Problems
Answer: option 1

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Problems
Answer: option 1

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In terms
of side, a
In terms of
altitude, h
Side - 2h/ √3
Altitude √3a/2 -
Circumradius a/√3 2/3 h
Inradius a/2√3 1/3 h
Area √3a2 /4 h2/√3
Special Triangles –EquilateralTriangle

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Problems
Answer: option B

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Polygons and their properties
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Parameter Properties
Sum of external angles 360
Sum of internal angles (n-2)180
No of sides
360
𝑒𝑥𝑡. 𝑎𝑛𝑔𝑙𝑒
No of diagonals 𝑛 𝑛 − 3
2
Area
Hexagon = 3√3
𝑎2
2
Octagon = 2a2 (1+ √2)
Polygons

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The points of a six-pointed star consist of six identical equilateral
triangles, with each side 6 cm (see figure). What is the area of the
shaded region?
A. 54 3
B. 48 3
C. 64 3
D. 84 3
E. 108 3
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6cm 6cm
Problems