College Geometry Online, eLearning

Angles 45, 90, 135, Theorems and Problems - Table of Content

Angle 45, 90, 135, Theorems and Problems

 

Geometry Problem 1548

Geometry Problem 1548: Exploring Segment DE Length in Triangle ABC with a 45-Degree Angle and Intersecting Altitudes

Geometry Problem 1544

Geometry Problem 1544: Challenge: Calculate the Area of a Triangle with Given Arc and Semicircle Intersections.

Geometry Problem 1520

Geometry Problem 1520 and a Thematic Poem.
Discovering Distances in a Rectangle with an Exterior Point: A Geometry Challenge.

Geometry Problem 1517

Geometry Problem 1517 and a Thematic Poem.
Unlocking Triangle Side Length: Solving with a Median and Two Angles. Difficulty Level: High School.

Dynamic Geometry 1483

Geometry Problem 1483.
Isosceles Right Triangle, Excenter, Perpendicular, Measurement.

Problem 1416

Geometry Problem 1416.
Right Triangle, Altitude, Incircle, Excircle, Tangency Points, 45 Degree Angle.

Problem 1413

Geometry Problem 1413.
Right Triangle, Incircle, Excircle, Tangency Points, Isosceles Right Triangle.

Problem 1412

Geometry Problem 1412.
Right Triangle, Incircle, Excircle, Tangency Points, 45 Degree Angle.

Problem 1411

Geometry Problem 1411.
Right Triangle, Incircle, Excircle, Tangency Points, Isosceles Right Triangle.

Problem 1410

Geometry Problem 1410.
Right Triangle, Incircle, Excircle, Tangency Points, 45 Degree Angle.

Problem 1401

Geometry Problem 1401.
Right Triangle with three circles on the sides, Isosceles, Diameter, Center, Tangent, Congruence.

Geometry problem 1364

Geometry Problem 1364.
Square, Inscribed Circle, Area, Angle Bisector, Perpendicular, 45 Degrees, Sketch, iPad Apps.

Geometry problem 1363

Geometry Problem 1363.
Square, Angle Bisector, Perpendicular, 45 Degrees, Angle, Sketch, iPad Apps.

Geometry problem 1338

Problem 1338.
Four Squares, Diagonals, Angle, 45 Degrees, Areas.

Geometry problem 1330

Geometry Problem 1330.
Two Squares Side by Side, Parallel, 45, 90 Degrees.

Geometry problem 1324

Geometry Problem 1324.
Quadrilateral, Diagonal, 45 Degrees, Angle Bisector, Isosceles Triangle, Congruence.

Geometry problem 1292

Geometry Problem 1292.
Square, Circle, Right Triangle, Arc, Inradius, Radius, Incircle, Measurement.

Geometry problem 1286

Geometry Problem 1286.
Triangle, Quadrilateral, 60, 135, 105 Degree Angles, Congruence, Measurement.

Geometry problem 1280

Geometry Problem 1280.
Quadrilateral, Perpendicular Diagonals, Isosceles Right Triangles, 45 Degrees, Collinear Points.

Geometry problem 1211

Geometry Problem 1211
Right Triangle, Altitude, Angle Bisector, 45 Degrees.

Geometric Art of Problem 109 using Mobile Apps

Geometric Art of Problem 109 using Mobile Apps.

Geometry Problem 1111

Geometry Problem 1111.
Right Triangle, External Squares, Cathetus, Angle Bisector, Area, Geometric Mean.

Geometry Problem 1110

Geometry Problem 1110.
Right Triangle, External Squares, Catheti, Cathetus, Angle Bisector, 45 Degree, Internal Square.

Geometry Problem 1109

Geometry Problem 1109.
Right Triangle, External Squares, Catheti, Cathetus, 45 Degree, Angle.

Geometry Problem 1084

Geometry Problem 1084.
Circle, Chord, Radius, Diameter, Parallel lines, 45 Degrees, Metric Relations.

Geometry Problem 1076

Geometry Problem 1076.
Square, 45 Degrees, Angle, Sum, Distance, Auxiliary Construction.

Geometry Problem 1016

Geometry Problem 1016.
Triangle, 45 Degrees, Area, Triangle, Quadrilateral, Altitude, Bisector.

Geometry Problem 1014

Geometry Problem 1014.
Square, Diagonal, 45 Degrees, Angle, Equal Areas, Triangle, Quadrilateral.

Geometry Problem 986

Geometry Problem 986.
Triangle, Median, Midpoint, Equal Angles, 45 Degrees.

Geometry Problem 976

Geometry Problem 976.
Isosceles Right Triangle, 45 Degrees, Incenter, Angle Bisector, Hypotenuse.

Geometry Problem 975

Geometry Problem 975.
Isosceles Right Triangle, 45 Degrees, Angle Bisector, Hypotenuse.

Isosceles Right Triangle, Angles,18, 45 Degrees, Congruence, Perpendicular bisector

Geometry Problem 859
Isosceles Right Triangle, Angles,18, 45 Degrees, Congruence, Perpendicular bisector.

Isosceles Right Triangle, Cevian, Ratio 2:1, 45 Degrees, Congruence, Angles, Auxiliary Lines

Geometry Problem 858
Isosceles Right Triangle, Cevian, Ratio 2:1, 45 Degrees, Congruence, Angles, Auxiliary Lines.

Problem 856: Triangle, Median, Midpoint, Angles, 30, 45 Degrees, Congruence, Auxiliary Lines

Geometry Problem 857
Triangle, Median, Midpoint, Angles, 30, 45 Degrees, Congruence, Auxiliary Lines.

Rhombus, Circle

Proposed Problem 455.
Rhombus, Inscribed Circle, Angle, Chord, 45 Degrees.

Quadrilateral, 60, 75, 135 degrees

Proposed Problem 405.
Quadrilateral, 60, 75, and 135 degrees, Midpoint.

Square, 45 degrees

Proposed Problem 367.
Square, Angle, 45 degrees, Pythagoras, Congruence, Similarity.

Right triangle, Congruence, Angles

Proposed Problem 363.
Right triangle, Congruence, Angles.

Rhombus, Square 

Proposed Problem 354.
Rhombus, Square, 45 degrees.

Circle, Semicircle, Chord, Diameter

Proposed Problem 311.
Circle Inscribed in a Semicircle, Chord, Diameter.
45 degree angle.

Circle inscribed in a semicircle

Proposed Problem 310.
Circle Inscribed in a Semicircle, 45 degree angle.

Triangle and angle bisector of 90 degrees

Proposed Problem 303.
Triangle, Angle bisector of 90 degrees, 45 degree angle.

Inscribed Quadrilateral

Proposed Problem 293.
Inscribed Quadrilateral, Perpendicular, Rectangle, Isosceles Right triangle, Area, Similarity, 45 degree angle.

Regular Octagon 

Proposed Problem 287: Regular Octagon. 45 degree angle.

Right Triangles, Formulas and Facts
Pythagorean theorem, Similarity, Geometric mean, hypotenuse, catheti (legs), semiperimeter, altitude, median, similar shapes areas, centers, orthocenter, incenter, centroid, circumcenter, radius, inradius, circumradius, exradius, circles, incircle, circumcircle, excircle.
45-45-90 Right triangle.

Octagon Index

Octagons.45, 135 degree angle

Square, Circle, 90 Arc

Proposed Problem 276.
Square, 90 degree Arcs, Circle, Radius, 45 degree angle.

Rectangle, Isosceles Right Triangle, Square, Area

Proposed Problem 252.
Rectangle, isosceles right triangle, square, area. 45 degree angle.

Elearning 244: Square center, diagonal

Proposed Problem 244. Square, Diagonals, Centers, Distance, 45 degree angle.

Square, Midpoint, Congruence, Pythagoras

Proposed Problem 239. Square, Midpoints, Lines, Congruence, Pythagoras, 45 degree angle.

Elearning 189

Proposed Problem 189. Squares, Distances, 45 degree angle.  

Elearning 188

Proposed Problem 188. Square, Diagonal, 45 Degrees Angle.  

Elearning 187: Right triangle, incircles, angles

Proposed Problem 187. Right Triangle, Altitude, Incenters, Circles, Angles, 45 degree angle.  

Elearning 186: Right triangle, circles

Proposed Problem 186. Right Triangle, Altitude, Incenters, Circles, 45 degree angle.  

Elearning 186: Right triangle, circles

Proposed Problem 186. Right Triangle, Altitude, Incenters, Circles, 45 degree angle.  

Overlapping circles, Angle

Proposed Problem 182. Overlapping Circles, Find an angle, 45 degree angle.  

Circular Sector 90 degree

Proposed Problem 181. Circular Sector of 90 degrees, 45-135 degree angle, find an angle.  

Rhombus, Square, Angle

Proposed Problem 179. Rhombus, Square, Diagonal, 45 degree angle.  

Bottema Theorem. Elearning.

Bottema's Theorem:
Triangle and Squares with Interactive Geometry Software
Step-by-Step construction, Manipulation, and animation,
45 degree angle.

Area of Square and triangle, Elearning.

Proposed Problem 112. Area of square and triangle, 45 degree angle.

Problem 109. Elearning.

Proposed Problem 109. Angles, Right Triangle, Cevian, 45 degree angle.

Proposed Problem 62: Square Diagonal, Inscribed Circle, 45 degree angle.

Hippocrates and Squaring the Circle
45 degree angle 

Proposed Problem 47. Angles and triangles, 45 degree angle.

Proposed Problem 33.
Triangle and quadrilateral,
45 degree angle.

Problem 31. Right Triangle, Incircle, Collinears, 45 degree angle.

Proposed Problem 29.
Right Triangle, altitude, incircle and inradius. Ten conclusions.
Geometry Problem Help 45-45-90 Right triangle

Proposed problem 19
Right Triangle and Excenter,
45 degree angle

Triangle, median, 45 degree angle

Problem 3. Triangle, median and angles, 45 degree angle.

Triangle, Median, 45 degree

Problem 1. Triangle, median and angles, 45 degree angle.

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Last updated: Jul 21, 2023