1) The document discusses polygons and their properties including the sum of interior angles.
2) It provides examples of regular polygons such as equilateral triangles, squares, pentagons and hexagons where all sides and angles are equal.
3) It works through an example calculating the three angles at vertex D of a regular pentagon ABCDE where each interior angle is 1080.
Mathematics: Regular and Irregular ShapesLorenKnights
Use mathematical language to explain the difference between regular and irregular shapes. Regular shapes have sides and angles that are all equal. Irregular shapes have sides and angles of different measures.
Mathematics: Regular and Irregular ShapesLorenKnights
Use mathematical language to explain the difference between regular and irregular shapes. Regular shapes have sides and angles that are all equal. Irregular shapes have sides and angles of different measures.
CIRCLE
DEFINITION AND PROPERTIES OF A CIRCLE
A circle can be defined in two ways.
A circle: Is a closed path curve all points of which are equal-distance from a fixed point called centre OR
- Is a locus at a point which moves in a plane so that it is always of constant distance from a fixed point known as a centre.
Regular N-gonal Right Antiprism: Application of HCR’s Theory of PolygonHarish Chandra Rajpoot
A regular n-gonal right antiprism is a semiregular convex polyhedron which has 2n identical vertices all lying on a sphere, 4n edges, and (2n+2) faces out of which 2 are congruent regular n-sided polygons, and 2n are congruent equilateral triangles such that all the faces have equal side. The equilateral triangular faces meet the regular polygonal faces at the common edges and vertices alternatively such that three equilateral triangular faces meet at each of 2n vertices. This paper presents, in details, the mathematical derivations of the generalized and analytic formula which are used to determine the different important parameters in terms of edge length, such as normal distances of faces, normal height, radius of circumscribed sphere, surface area, volume, dihedral angles between adjacent faces, solid angle subtended by each face at the centre, and solid angle subtended by polygonal antiprism at each of its 2n vertices using HCR’s Theory of Polygon. All the generalized formulae have been derived using simple trigonometry, and 2D geometry which are difficult to derive using any other methods.
Identify and name polygons based on their number of sides, and whether they are concave or convex, and whether they are equilateral, equiangular, or regular.
Calculate the measures of interior and exterior angles of polygons.
Biological screening of herbal drugs: Introduction and Need for
Phyto-Pharmacological Screening, New Strategies for evaluating
Natural Products, In vitro evaluation techniques for Antioxidants, Antimicrobial and Anticancer drugs. In vivo evaluation techniques
for Anti-inflammatory, Antiulcer, Anticancer, Wound healing, Antidiabetic, Hepatoprotective, Cardio protective, Diuretics and
Antifertility, Toxicity studies as per OECD guidelines
Embracing GenAI - A Strategic ImperativePeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
For more information, visit-www.vavaclasses.com
Francesca Gottschalk - How can education support child empowerment.pptxEduSkills OECD
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Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
Introduction to AI for Nonprofits with Tapp NetworkTechSoup
Dive into the world of AI! Experts Jon Hill and Tareq Monaur will guide you through AI's role in enhancing nonprofit websites and basic marketing strategies, making it easy to understand and apply.
2. sum of angles of a polygon
sum of exterior angles of a polygon
= (n-2) 1800
= 3600
3. sum of angles
if all angles are equal, then
each angle
= 1800
= 180 ÷ 3
=600
4. A triangle with equal sides and equal
angles is called a equilateral
triangle
5. sum of angles
if all angles are equal, then
each angle
= (n-2) 1800
= (4-2) 1800
= 2 × 1800
= 3600
=3600 ÷ 4
=900
6. A square is a quadrilateral with
all sides and all angles are
equal.
7. sum of angles
if all angles are equal, then
each angle
= (n-2) 1800
= (5-2) 1800
= 3 × 1800
= 5400
=5400 ÷ 5
=1080
8. A pentagon with equal sides and
equal angles is called regular
pentagon
9. sum of angles
if all angles are equal, then
each angle
= (n-2) 1800
= (6-2) 1800
= 4 × 1800
= 7200
=7200 ÷ 6
=1200
10. A hexagon with equal sides
and equal angles is called a
regular hexagon
11. A polygon with equal sides
and equal angles is called a
regular polygon.
12. A B
C
D
E
ABCDE is a regular
pentagon. Calculate
the three angles at
vertex D.
13. since ABCDE is a regular
pentagon , all sides and all
angles are equal and each
angle = 1080
∆AED and ∆BCD are isocelus
triangles
<EAD = <EDA = 180 - 108
2
=72 ÷ 2
= 360
A B
C
D
E
14. A B
C
D
E
since ABCDE is a regular pentagon ,
all sides and all angles are equal and
each angle = 1080
∆AED and ∆BCD are isocelus
triangles
<EAD = <EDA = 180 - 108
=72 ÷ 2
= 360
Similarly , <BDC = <CBD = 360
total angle at D = 1080
2
so,
<ADB = 1080-(360+360)
=360
15. In a regular pentagon
ABCDE the diagonals
drawn from a vertex to
the oppoite vertices
divide the angle into 3
equal angles.
A B
C
D
E
16. One angle of a regular
polygon is 1440.How many
sides does this polygon
has?
