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This document defines key terms and theorems related to triangles, including isosceles, equilateral, and right triangles. It defines base angles, vertex angles, the base angle theorem, converse of the base angle theorem, and corollaries relating equilateral and equiangular triangles. It also defines the hypotenuse-leg congruence theorem for right triangles.
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This document discusses theorems related to isosceles triangles. It defines an isosceles triangle as one with at least two congruent sides and identifies the parts of an isosceles triangle. The Isosceles Triangle Theorem states that if two sides of a triangle are congruent, then the angles opposite those sides are also congruent. There are corollaries that an equilateral triangle is equiangular with three 60-degree angles and that the bisector of the vertex angle of an isosceles triangle is perpendicular to the base at its midpoint.
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This document summarizes theorems about isosceles triangles. An isosceles triangle has at least two congruent sides called legs and one different side called the base. If two sides of a triangle are congruent, then the angles opposite those sides are also congruent. Additionally, if two angles of a triangle are congruent, then the sides opposite those angles must be congruent as well.
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This document discusses properties of isosceles triangles. It states that an isosceles triangle has at least two sides of equal length. The base angles of an isosceles triangle are always congruent. If a triangle has two congruent angles, then it is an isosceles triangle. An equilateral triangle is a special type of isosceles triangle where all three sides are congruent and all three angles are congruent.
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1) A triangle is a three-sided polygon with three vertices and three edges.
2) Triangles can be classified based on side lengths (equilateral, isosceles, scalene) or interior angles (right, acute, obtuse).
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This document outlines different methods for proving that two triangles are congruent:
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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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The document discusses different types of triangles based on the lengths of their sides: equilateral triangles have all three sides equal; isosceles triangles have two equal sides; scalene triangles have no equal sides. It also describes criteria for determining if two triangles are congruent, including side-angle-side (SAS), angle-side-angle (ASA), and side-side-side (SSS). Properties of triangles are outlined, such as the angle sum property that the interior angles sum to 180 degrees and the exterior angle property relating an exterior angle to the two interior angles. The Pythagorean theorem relating the sides of a right triangle is presented along with Heron's formula for calculating the area of any triangle.
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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.
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The document discusses different types of triangles and rules for determining if triangles are congruent. It defines congruent figures as those that are equal in size and shape and can cover each other completely. It then provides four rules for triangle congruence: SAS, ASA, SSS, and RHS. These rules state that triangles are congruent if their corresponding sides and/or angles are equal.
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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.
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The document discusses triangles and their properties. It defines a triangle as a three-sided polygon and describes the three types of triangles based on their sides: equilateral, isosceles, and scalene. It then covers triangle properties such as the angle sum theorem, exterior angle theorem, and Pythagorean theorem. The document also discusses secondary parts of triangles like medians, altitudes, angle bisectors, and perpendicular bisectors. It concludes with criteria for triangle congruency and formulas for calculating triangle area.
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This document discusses congruence of triangles in mathematics. It defines congruence as two shapes being equal in shape, size, and area or coinciding exactly when placed on top of each other. There are five criteria for triangle congruence: side-side-side (SSS), side-angle-side (SAS), angle-angle-side (AAS), angle-side-angle (ASA), and right-angle-hypotenuse-side (RHS). Each rule states that if the given sides or angles are equal, then the triangles are congruent. Examples are provided to illustrate each rule.
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The document discusses different types of triangles and rules for determining if triangles are congruent. It defines congruent figures as those that are equal in size and shape and can cover each other completely. It then provides four rules for triangle congruence: SAS, ASA, SSS, and RHS. These rules state that triangles are congruent if their corresponding sides and/or angles are equal.
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2.1 terms
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10.3 terms
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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.
8.2 terms
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9.2 terms
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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.
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.
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.
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.
6.3 terms
This document outlines five theorems that can prove if a quadrilateral is a parallelogram: if both pairs of opposite sides are congruent; both pairs of opposite angles are congruent; an angle is supplementary to both of its consecutive angles; the diagonals bisect each other; or one pair of opposite sides are congruent and parallel. It also summarizes the key properties of a parallelogram - both pairs of opposite sides are parallel and congruent, both pairs of opposite angles are congruent, or the diagonals bisect each other.
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ここ3000字までしか入らないけどタイトルの方がたくさん文字入ると思います。
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みなさんこんにちはこれ何文字まで入るの？40文字以下不可とか本当に意味わからないけどこれ限界文字数書いてないからマジでやばい文字数いけるんじゃないの？えこ...
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4.6 terms
- 1. Terms of Endearment Isosceles, Equilateral, and Right Triangles: 4.6