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




Geometry Problem 1570:
Calculating BE in Overlapping Squares: A High School and College Geometry Challenge. 

Geometry Problem 1564:
Find the Area of Quadrilateral BGDJ in a Right Triangle involving the Altitude, Angle bisectors, and Midpoints. 

Geometry Problem 1563:
Perpendicularity in a Right Triangle involving the Altitude, Angle bisectors, and Midpoints. 

Geometry Problem 1562:
Proof of Collinearity in a Rightangled Triangle involving the Altitude, Angle bisectors, and Midpoint. 

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

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

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

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

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

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

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

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

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

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

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

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

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

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


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

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

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

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

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

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

Geometric Art of Problem
109 using Mobile Apps. 

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Proposed Problem 363.
Right triangle, Congruence, Angles. 

Proposed Problem 354.
Rhombus, Square, 45 degrees. 

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

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

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

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

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.
454590 Right triangle. 

Octagons.45, 135 degree
angle 

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

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

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


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


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


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


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

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

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

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


Proposed Problem 181. Circular
Sector of 90 degrees,
45135 degree angle, find an angle.


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


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

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


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 454590 Right triangle 

Proposed problem 19
Right Triangle and Excenter,
45 degree angle 

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

Problem
1. Triangle, median and angles,
45 degree angle. 
Home 
Search  Geometry

Post a comment 
Email Last updated:
Jul 26, 2024
