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This document defines and classifies different types of triangles based on their sides and angles. It discusses equilateral, isosceles, scalene, acute, right, obtuse, and equiangular triangles. Key properties are also summarized, such as the triangle sum theorem stating the interior angles sum to 180 degrees, and the exterior angle theorem relating exterior and interior angles.
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This document provides definitions and properties related to triangles:
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This document discusses how triangles can be classified into different types based on the length of their sides or the measure of their angles. Triangles are classified based on side length as equilateral, isosceles, or scalene, and based on angle measure as acute, right, obtuse, or equiangular.
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A triangle is a polygon formed by joining three non-collinear points. Triangles can be classified based on their side lengths or angles. There are three types of triangles based on sides: equilateral (all sides equal), isosceles (two sides equal), and scalene (all sides unequal). Based on angles, triangles are right (one 90 degree angle), acute (all angles less than 90 degrees), or obtuse (one angle greater than 90 degrees). A triangle is thus defined as a three-sided polygon where the sum of the interior angles is 180 degrees.
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Triangles are three-sided polygons that come in three types based on their side lengths: equilateral triangles have all three sides the same length, isosceles triangles have two sides the same length, and scalene triangles have all three sides of different lengths. The area of any triangle can be calculated using Hero's Formula, which uses the triangle's side lengths and semi-perimeter. While Pascal's Triangle is named after Blaise Pascal, he did not invent the triangle - other mathematicians studied and used triangular patterns before him.
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There are four types of triangles: equilateral triangles have three equal sides and three equal angles; isosceles triangles have two equal sides and two equal angles; scalene triangles have no equal sides and all different angles; right-angled triangles contain one 90 degree angle and can be either isosceles or scalene.
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A triangle is a simple closed shape with three sides and three angles. Triangles can be categorized based on side length as scalene (all sides unequal), isosceles (two sides equal), or equilateral (all three sides equal). They can also be categorized based on angle measures as acute (all angles less than 90 degrees), right (one angle is 90 degrees), or obtuse (one angle greater than 90 degrees). Key properties of triangles include that the three interior angles sum to 180 degrees and that the longest side has the largest opposite interior angle.
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Presentation Math In The Real World
This geometry project presentation covers various geometric shapes and terms including points, lines, planes, angles, triangles, quadrilaterals, circles, cylinders, spheres, and pyramids. Key geometric concepts that will be discussed are undefined terms in geometry, different types of lines and their properties, various polygons defined by their number of sides, as well as circles, cylinders, spheres, and how triangles are classified by their angle measures.
Geometry in the Real World Project (Mrs. Sykes)
The document defines and describes basic geometric shapes and terms including points, lines, planes, angles, triangles, quadrilaterals, circles, spheres, cylinders, cones, and pyramids. It provides definitions for common shapes such as squares, rectangles, trapezoids, and parallelograms. It also introduces polygons with specific numbers of sides such as triangles, pentagons, hexagons, and octagons.
Dan opowerpoint
This document provides definitions and concepts related to triangles and angles in geometry. It defines different types of triangles based on sides and angles, including equilateral, isosceles, scalene, acute, and right triangles. It discusses parts of a triangle including vertices, adjacent sides, and opposite sides. The document also covers finding angle measures using properties of triangles, angle bisectors, theorems about congruent and complementary angles, medians of triangles, and the relationship between side lengths and angle measures.
Geometry In The Real World
This document defines and describes basic geometric shapes and terms including points, lines, planes, angles, triangles, quadrilaterals, circles, cylinders, spheres, and other polygons. Key geometric concepts covered are lines, planes, angles, perpendicular and parallel lines, triangles, squares, rectangles, trapezoids, parallelograms, circles, cylinders, spheres, octagons, cubes, and hemispheres.
Geometry In The Real World
This document defines and describes basic geometric shapes and terms including points, lines, planes, angles, triangles, quadrilaterals, circles, cylinders, spheres, and other polygons. It provides definitions for fundamental geometric objects and their characteristics in only a sentence or two per term to concisely outline key concepts in geometry.
Geometry in the Real World
This document defines and describes basic geometric shapes and terms including points, lines, planes, angles, triangles, quadrilaterals, circles, cylinders, spheres, and other polygons. Key geometric concepts covered are undefined terms, lines and their components, angles, perpendicular and parallel lines, properties of triangles, quadrilaterals, circles, cylinders, spheres, and other common polygons.
Triangles What are the properties of an Isosceles Triangle.pdf
The document defines and describes properties of isosceles triangles. It begins by classifying triangles into three types based on side lengths: equilateral, scalene, and isosceles. It then discusses properties specific to isosceles triangles, including that they have two equal sides or legs and an unequal base, and angles opposite the equal sides are also equal. Several formulas are provided for calculating properties of isosceles triangles like area, perimeter, and altitude. Examples of isosceles triangles in real life and practice problems with solutions are also included.
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Triangles What are the properties of an Isosceles Triangle.pdf
Triangles What are the properties of an Isosceles Triangle.pdf
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Inductive reasoning & logic
Inductive reasoning uses examples and observations to reach a conclusion, called a conjecture. A conjecture is either always true or false. While examples can support a conjecture, they cannot prove it. A counterexample can demonstrate that a conjecture is false.
10.1 terms
The document defines key terms related to circles and tangents, including: a circle as points equidistant from a center point; a radius and diameter; a chord as a segment with endpoints on the circle; a secant as a line intersecting a circle at two points; and a tangent as a line intersecting a circle at exactly one point. It states that a tangent line is perpendicular to the radius drawn to the point of tangency, and that for two segments from the same exterior point to both be tangent to a circle, they must be congruent.
9.1 terms
Triangles formed by drawing an altitude to the hypotenuse of a right triangle are similar to the original triangle and each other. The altitudes of a right triangle act as geometric means for the similar triangles, with the leg altitudes being geometric means between the close short segment and full base, and the right angle altitude being the geometric mean between the two parts it creates on the hypotenuse.
6.1 terms
This document defines and describes various types of polygons including: convex polygons which have no interior angles, concave polygons which have interior angles, equilateral polygons with all sides congruent, equiangular polygons with all interior angles congruent, and regular polygons which are both equilateral and equiangular. It also defines vertices, diagonals, and explains the interior angle sum theorem for quadrilaterals.
8.6 terms
This document discusses proportional relationships in triangles. It states that if a line parallel to one side of a triangle intersects the other two sides, it divides them proportionally. It also states that if three parallel lines intersect two transversals, they divide the transversals proportionally. Finally, it notes that if a ray bisects an angle of a triangle, it divides the opposite side proportionally to the lengths of the other two sides.
11.2 terms
This document discusses how to calculate the areas of regular polygons such as equilateral triangles and other shapes. It explains that the area of an equilateral triangle is (side^2) * √3/4 and the area of a regular polygon is (1/2) * apothem * perimeter. The apothem is the distance from any side to the center and the central angle is found by dividing 360 by the number of sides.
8.5 terms
Two methods for proving triangles are similar are presented: SSS similarity, where all corresponding sides between two triangles are proportional, proving the triangles are similar; and SAS similarity, where two corresponding sides of two triangles are proportional and the included angle is congruent, also proving the triangles are similar.
8.2 terms
This document discusses proportions and their properties in geometry. A proportion is two equal ratios that can be set up and cross-multiplied to solve for unknown values. The terms of a proportion can be switched diagonally or by adding denominators to numerators while maintaining equality. The geometric mean is the value diagonal to itself in a proportion of two positive numbers.
6.2 terms
A parallelogram is a quadrilateral with both pairs of opposite sides parallel. The properties of a parallelogram are that if it is a parallelogram, its opposite sides are congruent, its opposite angles are congruent, consecutive angles are supplementary, and its diagonals bisect each other.
6.7 terms
This document discusses the formulas for calculating the areas of various shapes. It states that congruent polygons have the same area, and the area of a region is the sum of non-overlapping areas. It then provides the area formulas for a square, rectangle, parallelogram, triangle, trapezoid, kite, and rhombus. For a rhombus, it notes that the area can also be calculated as for a parallelogram using base times height.
6.4 terms
This document defines and compares properties of rhombuses, rectangles, and squares. A rhombus is a parallelogram with 4 congruent sides and perpendicular diagonals. A rectangle is a parallelogram with 4 right angles and congruent diagonals. A square has the combined properties of a rhombus, rectangle, and parallelogram - it is a rhombus and rectangle with 4 equal sides and right angles.
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.
9.6 terms
This document provides instructions for solving right triangles using trigonometric functions. It explains that solving a right triangle involves finding the measures of the three angles and lengths of the three sides. It notes that a calculator's inverse trigonometric functions allow working backwards from a trig ratio to the corresponding angle measure. Finally, it offers guidance for determining which inverse function to use based on the given information, such as using tangent when the hypotenuse is unknown or cosine when the opposite side is missing.
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.
11.4 terms
This document discusses formulas for circumference and arc length. It states that circumference C equals 2πr or πd, where r is the radius and d is the diameter. It also explains that arc length is calculated as a percentage of the circumference by taking the arc measure in degrees and dividing by 360, then multiplying that fraction by the circumference.
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.
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4.1 terms
- 1. Terms of Endearment Triangles and Angles: 4.1