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This document introduces perimeter, circumference, and area formulas for common shapes including squares, rectangles, triangles, and circles. It states that for squares the perimeter is 4 times the side length and the area is the side length squared. For rectangles, the perimeter is twice the length plus twice the width, and the area is length times width. For triangles, the perimeter is the sum of the three sides and the area is half the base times the height. For circles, the circumference is 2πr and the area is πr2, where π is approximately 3.14 and r is the radius.
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10.4 terms
If lines intersect within or on the edge of a circle, the measure of the angles formed can be determined based on the intercepted arcs. For intersections inside the circle, the angle measure is half the sum of the intercepted arcs. For intersections on the edge of the circle, the angle measure is half the intercepted arc. For intersections outside the circle, the angle measure is half the difference of the intercepted arcs.
10.2 terms
The document discusses key concepts relating to arcs and chords in circles. It defines a central angle as an angle whose vertex is the center of the circle, with the measure of its corresponding arc being equal to the angle's degrees. Arcs are classified as minor, major, or semicircles based on their angle measures. Adjacent arcs can be added together to find the measure of a larger arc. There are several theorems stated about relationships between arcs, chords, diameters, and angles, such as congruent arcs corresponding to congruent chords, diameters bisecting chords and angles if perpendicular to a chord, and chords being congruent if equidistant from the center.
6.5 terms
This document defines and provides key details about trapezoids, isosceles trapezoids, the midsegment of a trapezoid, and kites. It states that a trapezoid has one pair of parallel sides called bases, and the other sides are called legs. An isosceles trapezoid has congruent legs and congruent base angles. The midsegment of a trapezoid connects the midpoints of the legs and is parallel to the bases. A kite has two pairs of consecutive congruent sides but opposite sides are not congruent, and its diagonals are perpendicular with one pair of opposite angles being congruent.
11.5 terms
The document discusses calculating the areas of circles and sectors. It states that the area of a circle is calculated as A = πr2, and the area of a sector is calculated as (Arc Measure/360)(area of the full circle), which finds the percentage of the total circular area that the sector represents by dividing the arc measure in degrees by 360.
11.1 terms
The document discusses angle measures in polygons. It states that the sum of interior angles in any polygon is (n-2)180, where n is the number of sides. It also explains that the sum of exterior angles is always 360, and each exterior angle is calculated as 360/n, where n is again the number of sides.
10.3 terms
This document discusses inscribed angles and their relationship to circles. It states that an inscribed angle is an angle whose vertex is on a circle and whose sides contain chords of the circle. It also notes that an inscribed angle measures half the degrees of its intercepted arc and that two inscribed angles intercepting the same arc together measure the full arc. Additionally, it mentions that if a right triangle is inscribed in a circle, its hypotenuse is the diameter of the circle and that a quadrilateral can be inscribed in a circle if and only if its opposite angles are supplementary.
9.5 terms
This document provides information about trigonometric ratios and using a calculator to evaluate trigonometric functions. It defines the sine, cosine, and tangent ratios using the SOHCAHTOA mnemonic. It also explains that calculators may require typing the trig function before or after the number, and some may not require hitting the equals sign, so it is important to know how to use the specific calculator.
10.6 terms
The standard equation for a circle is (x-h)2 + (y-k)2 = r2, where (h,k) represents the center of the circle and r represents the radius. When solving for the center or radius, the terms in the parentheses change signs - the x and y terms change to the opposite of the center coordinates h and k, and the radius r is the square root of the number after the equals sign.
9.2 terms
The Pythagorean Theorem states that for any right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. It is represented by the equation a2 + b2 = c2, where a and b are the legs of the right triangle and c is the hypotenuse. A Pythagorean triple refers to three positive integers that satisfy the Pythagorean Theorem and can be used as the sides of a right triangle, such as 3, 4, and 5.
8.1 terms
A ratio is a fraction that compares two quantities, such as the ratio of a to b written as a/b. A proportion is when two ratios are equal to each other, allowing the fractions to be cross-multiplied and canceled out. Ratios and proportions use fractions to compare relationships between quantities.
6.6 terms
This document presents a hierarchy of quadrilaterals in a grid structure, with each shape below sometimes being a type of the shape above it, and each shape above always being a type of the shapes below it since they share characteristics. Kite is at the top and is sometimes a parallelogram, rectangle, square, rhombus or trapezoid. Parallelogram is sometimes a rectangle, square or rhombus. Trapezoid is sometimes an isosceles trapezoid.
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Syllabus
Chapter-1
Introduction to objective, scope and outcome the subject
Chapter 2
Introduction: Scope and Specialization of Civil Engineering, Role of civil Engineer in Society, Impact of infrastructural development on economy of country.
Chapter 3
Surveying: Object Principles & Types of Surveying; Site Plans, Plans & Maps; Scales & Unit of different Measurements.
Linear Measurements: Instruments used. Linear Measurement by Tape, Ranging out Survey Lines and overcoming Obstructions; Measurements on sloping ground; Tape corrections, conventional symbols. Angular Measurements: Instruments used; Introduction to Compass Surveying, Bearings and Longitude & Latitude of a Line, Introduction to total station.
Levelling: Instrument used Object of levelling, Methods of levelling in brief, and Contour maps.
Chapter 4
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Chapter 5
Transportation: Introduction to Transportation Engineering; Traffic and Road Safety: Types and Characteristics of Various Modes of Transportation; Various Road Traffic Signs, Causes of Accidents and Road Safety Measures.
Chapter 6
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Water Pollution: Water Quality standards, Introduction to Treatment & Disposal of Waste Water. Reuse and Saving of Water, Rain Water Harvesting. Solid Waste Management: Classification of Solid Waste, Collection, Transportation and Disposal of Solid. Recycling of Solid Waste: Energy Recovery, Sanitary Landfill, On-Site Sanitation. Air & Noise Pollution: Primary and Secondary air pollutants, Harmful effects of Air Pollution, Control of Air Pollution. . Noise Pollution Harmful Effects of noise pollution, control of noise pollution, Global warming & Climate Change, Ozone depletion, Greenhouse effect
Text Books:
1. Palancharmy, Basic Civil Engineering, McGraw Hill publishers.
2. Satheesh Gopi, Basic Civil Engineering, Pearson Publishers.
3. Ketki Rangwala Dalal, Essentials of Civil Engineering, Charotar Publishing House.
4. BCP, Surveying volume 1
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