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Triangles

Prove Angle Pair Relationships

Subject: 
Geometry
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Triangles
Angle
Congruence

??? ? ,ESSON?????s?'EOMETRY?.OTETAKING?'UIDE? #OPYRIGHT???-C$OUGAL?,ITTELL?(OUGHTON?-IFFLIN?#OMPANY? ??? 0ROVE?!NGLE?0AIR?2ELATIONSHIPS 'OAL? +?5SE?PROPERTIES?OF?SPECIAL?PAIRS?OF?ANGLES? 4(%/2%-????? ? ?2)'(4?!.',%3?#/.'25%.#%? 4(%/2%- !LL?RIGHT?ANGLES?ARE?? V??}??i??? ? 4(%/2%-????? ? ?#/.'25%.4?3500,%-%.43? 4(%/2%- )F?TWO?ANGLES?ARE?SUPPLEMENTARY?TO?THE?? ? ? ? ? SAME?ANGLE??OR?TO?CONGRUENT?ANGLES ??? THEN?THEY?ARE?? V??}??i??? ? )F????AND????ARE?SUPPLEMENTARY?AND????AND????? ARE?SUPPLEMENTARY??THEN?????????? ? 4(%/2%-????? ? ?#/.'25%.4?#/-0,%-%.43? 4(%/2%- )F?TWO?ANGLES?ARE?COMPLEMENTARY?TO?THE?? ? ? ? ? SAME?ANGLE??OR?TO?CONGRUENT?ANGLES ??? THEN?THEY?ARE?? V??}??i??? ? )F????AND????ARE?COMPLEMENTARY?AND????AND????ARE? COMPLEMENTARY??THEN???{?????? ?

Precalc midterm study guide part 2

Subject: 
Trigonometry
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trigonometry
Triangle geometry
Triangles
Ratios
Trigonometric functions
Triangle
Solution of triangles
Proofs of trigonometric identities

Name:______________________________ Date:_____________________________ Midterm Review (continued) 53. Solve the triangle ABC given a = 9, b= 7, c = 5. 54. Solve the triangle ABC given a = 7, b=6, measure of angle A=26.3?. 55. Find the area of a triangle with sides 13, 15, 18. 56. Sketch a graph of the following trigonometric functions using the standard trig viewing window. f(x) = csc x f(x) = cot x f(x) = tan x f(x) = sec x 57. Evaluate 8 7tan,8 3cos,8 5sin ??? , sin 165?. 58. P(-5,-12) is on the terminal side of an angle in standard position with measure ,? where 0 < ? < 2?.

AHSME 1992

Subject: 
Algebra
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Mathematics
Abstract algebra
Integer sequences
Number theory
Triangles
Triangle geometry
Combinatorics
Number
Prime number
Triangle
Coprime
Integer
sports

USA AIME 1992 1 Find the sum of all positive rational numbers that are less than 10 and that have denominator 30 when written in lowest terms. 2 A positive integer is called ascending if, in its decimal representation, there are at least two digits and each digit is less than any digit to its right. How many ascending positive integers are there? 3 A tennis player computes her win ratio by dividing the number of matches she has won by the total number of matches she has played. At the start of a weekend, her win ratio is exactly .500. During the weekend, she plays four matches, winning three and losing one. At the end of the weekend, her win ratio is greater than .503. What?s the largest number of matches she could?ve won before the weekend began?

AHSME 1985

Subject: 
Algebra
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geometry
Euclidean geometry
Triangles
Triangle geometry
polyhedra
Triangle
Tetrahedron
Area
Right triangle
Tournament
American Invitational Mathematics Examination

USA AIME 1985 1 Let x1 = 97, and for n > 1 let xn = nxn?1 . Calculate the product x1x2 ? ? ?x8. 2 When a right triangle is rotated about one leg, the volume of the cone produced is 800pi cm3. When the triangle is rotated about the other leg, the volume of the cone produced is 1920pi cm3. What is the length (in cm) of the hypotenuse of the triangle? 3 Find c if a, b, and c are positive integers which satisfy c = (a+ bi)3 ? 107i, where i2 = ?1. 4 A small square is constructed inside a square of area 1 by dividing each side of the unit square into n equal parts, and then connecting the vertices to the division points closest to the opposite vertices. Find the value of n if the the area of the small square is exactly 1/1985. A B CD 1/n

Formula

Subject: 
Algebra
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geometry
Mathematics
Triangles
equations
Triangle geometry
Exponentials
Elementary algebra
Area
Volume
Surface area
Circle
Right triangle
Algebra
Formula

| COMMON?MATH?FORMULAS? AREA(A) Square Rectangle Parallelogram Triangle Circle Trapezoid Sphere ? ? ??; ? ? ??; ? ? ??; ? ? 1/2??; ? ? ???; ?? ? ?1/2???1? ? ??2???; ? ? 4??? where s = any side of the square where l = length and w = width where b = base and h = height where b = base and h = height where ?= 3.14 and r = radius where s= Surface area SURFACE AREA (SA)of a: cube SA = 6?? where s = any side cylinder (lateral) ?? ? 2???; where ?=3.14, r = radius, and h = height PERIMETER (P) of a Square ? ? 4?; where s = any side Rectangle ? ? 2? ? 2?; where l = length and w = width Triangle ? ? ?1 ? ?2 ? ?3; where s = a side

Geometry

Subject: 
Geometry
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geometry
Triangles
Triangle geometry
Euclidean plane geometry
Polygons
Quadrilaterals
Triangle
Euclidean geometry
Rectangle
Angle
Area
Circle

GRADUATE RECORD EXAMINATIONS? Math Review Chapter 3: Geometry Copyright ? 2010 by Educational Testing Service. All rights reserved. ETS, the ETS logo, GRADUATE RECORD EXAMINATIONS, and GRE are registered trademarks of Educational Testing Service (ETS) in the United States and other countries. ?

Geometry

Subject: 
Geometry
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geometry
Triangles
Triangle geometry
Euclidean plane geometry
Polygons
Quadrilaterals
Triangle
Euclidean geometry
Rectangle
Angle
Area
Circle

GRADUATE RECORD EXAMINATIONS? Math Review Chapter 3: Geometry Copyright ? 2010 by Educational Testing Service. All rights reserved. ETS, the ETS logo, GRADUATE RECORD EXAMINATIONS, and GRE are registered trademarks of Educational Testing Service (ETS) in the United States and other countries. ?

Geometry notes

Subject: 
Geometry
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Geometry
Triangle geometry
Euclidean geometry
Triangles
Triangle
Elementary geometry
SSS postulate
AA postulate
Technology
Tags: 
Triangles

Lesson 3.03 KEY Main Idea (page #) DEFINITION OR SUMMARY EXAMPLE or DRAWING Objective After completing this lesson, I will be able to: construct congruent triangles explain why the constructed triangles are congruent Constructing Congruent Triangles (P1-2) Congruent triangles may be constructed by hand using a COMPASS and STRAIGHTEDGE. Congruent triangle may also be constructed using computer technology such as GEOGEBRA. Constructing Congruent Triangles based on S-S-S Postulate (P3) ?ABC is congruent to ?DEF because segment f was constructed with the same length as segment b. Segment e was constructed with the same length as segment c, and segment d was constructed with the same length as segment a. By the SIDE-SIDE-SIDE postulate, ?ABC ?DEF.

Median, Centroid, Altitude, Orthocenter

Subject: 
Geometry
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Triangles

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