This document provides an overview of key geometry concepts covered in a lesson, including: 1) Classification of angles as acute, right, obtuse, or reflex 2) Properties of triangles such as internal angle sums, relationships between sides and angles, and triangle classification 3) Concepts of congruency, similarity, and properties of congruent and similar triangles 4) Special right triangles and their properties, including the Pythagorean theorem 5) Properties of polygons and calculations for polygon parameters and areas 6) Example problems are provided to demonstrate application of these concepts.

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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
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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