Triangles: Theorems and Problems 3


Three lines connect us,
Angles, sides, shapes unfold,
Triangle problems solved. 

Geometry Problem 1580:
60Degree Triangle Challenge: Uncover AD Using Excenter and Circumcircle Clues. 

Geometry Problem 1579:
Involving perpendicular diameters, tangents, and triangle areas. 

Geometry Problem 1578:
Find the Area of a Bicentric Quadrilateral with Perpendicular Extensions of Opposite Sides!. 

Geometry Problem 1577:
Prove that in triangle ABC, segment AB equals the sum of segments BD and CD, with given angles and congruent segments. 

Geometry Problem 1576:
Congruency of Segments in Triangle ABC with Angles 30 and 20 Degrees and an Interior Cevian 

Geometry Problem 1575:
Prove an Angle Bisector in a Triangle Involving an Altitude, Midpoint, and Excircle 

Geometry Problem 1574:
Triangle with Three Circles through a Point and the Concyclicity of Six Intersection Points 

Geometry Problem 1572:
Calculate Angle C with Geometric Methods Using Sides AB=17, BC=25, and Angle A=45 Degrees 

Geometry Problem 1571:
Prove that the intermediate angle in a Pythagorean Triple 72425 measures 74 degrees. 

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

Geometry Problem 1569:
Prove a Relationship: EG Equals the Incircle Diameter in Triangle ABC with Square CDEF. 

Geometry Problem 1568:
Concyclicity of Points B, D , H, J in a Triangle ABC with an Incircle and a Tangent Circle. 

Geometry Problem 1567:
Finding Tangent Distances in a Circumscribed Isosceles Trapezoid. 

Geometry Problem 1566:
Demonstrate AC Equals AE + CD in an Equilateral Triangle ABC Involving Cevians and 60 Degrees.. 

Geometry Problem 1565:
Find the Length of BF in Triangle ABC Involving Median, Perpendicular, Midpoint, and Congruence. 

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 1561:
Triangle ABC, Circumcenter O, Orthocenter H, Parallel Line, and Angle
Secrets. 

Geometry Problem 1560:
Trapezoid ABCD: Unlocking Angle Secrets at G and H. 

Geometry Problem 1559:
Proving BC Bisects Segment DE. This geometry problem challenges students at high school and college levels. 

Geometry Problem 1558:
The midpoints of segments connecting corresponding vertices of equilateral triangles form an equilateral triangle. 

Geometry Problem 1557:
Calculate the Angle DHG in Right Triangle ABC. The problem involves: equilateral,
isosceles, midpoint and congruence 

Geometry Problem 1556: Right Triangle ABC and Inscribed Circle. The problem involves circle, chords, tangent, perpendicular lines, and congruence 

Geometry Problem 1555: Find Length of DE. The problem involves chords, tangent, circles, and intersections of line 

Geometry Problem 1554: Finding the Length of Side AB in Triangle ABC 

Geometry Problem 1553: Solving for OC in Triangle ABC with Unique Angle Bisectors 

Geometry Problem 1552: Exploring Angle C in Triangle ABC with Given Angle A and Side Lengths 

Geometry Problem 1551: Unraveling Angle Relations in Cyclic Quadrilaterals: Solving for Angle GEJ: A High School Level Investigation 

Geometry Problem 1550: Solving for Segment BD: An Angle Puzzle in Right Triangle ABC: A High School Level Investigation 

Geometry Problem 1549: Unraveling the Geometric Mystery: Calculating Angle
BGE with the Incircle and Tangent in Triangle ABC 

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

Geometry Problem 1547: Tangents' Dance: Exploring BtoAC Distance in a
Circle's Grasp 

Geometry Problem 1546: Discover the Hidden Geometry: Calculate Area of Contact Triangle DEF in Triangle ABC 

Geometry Problem 1545: Unlock the Geometric Mystery: Calculate the Area of Triangle ABC with Inscribed Circle and Excenters! 

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

Geometry Problem 1543: Calculating the Area of Quadrilateral ABED in a Square with a Side Length of 20 and an Intersecting Arc. 

Geometry Problem 1542: Unraveling a Geometric Puzzle with a Circumscribed
Right Triangle and Square to the Same Circle for School and College. 

Geometry Problem 1541 Challenge: Unveiling BG Length in an Inscribed Quadrilateral with Harmonic Quaternary Insight for Academic Pursuit. 

Geometry Problem 1540: Solving for the Length of Chord in a Circle: Analyzing Intersections and Given Values for Academic Pursuits. 

Geometry Problem 1539 Demystified: Unraveling the Lengths in an Isosceles Triangle with Altitude and Tangent Secrets!. 

Geometry Problem 1538: Unlocking the Secrets of Triangular Geometry: Solve for the Area of a Quadrilateral Using External Squares and a Segment Length. 

Geometry Problem 1537 Challenge: Can You Solve for the Missing Area in a Parallelogram using Midpoints and Intersection Points?. 

Geometry
Problem 1536: Discover the Power of Midpoints: Solving for Missing Areas in Quadrilaterals. 

Geometry
Problem 1535: Crack the Code: Inscribed Circle in Square  Angle Challenge! Solve the Mystery. 

Geometry
Problem 1533: Discovering Relationships between Angles and Lines in an Exterior Right Triangle of a Square  A High School Challenge.
. 

Geometry
Problem 1532: Crack the Code of Geometry Problem 1532: How to Find the Angle in a Square with a Tangent Semicircle!  A High School Challenge.
. 

Geometry
Problem 1531: Discover How to Calculate the Length of a Chord in a Circle with Diameter Intersection and an Angle between the Diameter and Chord  A High School Challenge.
. 

Geometry
Problem 1530: Unlock the Secrets of Geometric Angles: Calculate the Measurement of an Angle in a Square and Rectangle Figure Today!  A High School Challenge.
. 

Geometry
Problem 1529: Unlock the Mystery of Triangles: Solving for the Missing Angle with 1005030 Degree Angles and Cevian Lengths  A High School Challenge.
. 

Geometry
Problem 1526: Mastering Geometry ProblemSolving: Discover the Distance Between Two Sides in a Parallelogram Using Bisectors and Distance Measures.
. 

Geometry
Problem 1525 and a Thematic Poem.
Unveiling the Secrets of an Equilateral Triangle in Right Triangle Geometry: Finding the Midpoint Distance between Segments. 

Geometry
Problem 1524 and a Thematic Poem.
Unlock the Mystery of Parallelograms: Discover the Length of Segment between the Intersecting Angle Bisectors. 

Geometry
Problem 1523 and a Thematic Poem.
Discover How to Calculate the Length of the Altitude in an Isosceles Triangle  Get Expert Geometry Tips Now!
. 

Geometry
Problem 1522 and a Thematic Poem.
Unlocking the Angle Measure of a Triangle with Median and Doubled Side Lengths. 

Geometry
Problem 1521 and a Thematic Poem.
Unlock the Secret to Finding the Measure of an Angle in a Triangle with Two Sides as Diameters of Circles. 

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

Geometry
Problem 1519 and a Thematic Poem.
Discover the Length of a Segment in a Parallelogram using Midpoints and Parallel Lines. 

Geometry
Problem 1518 and a Thematic Poem.
Boost Your Geometry Skills: Solve for the Number of Sides in an Equiangular Polygon with an Interior Point and Bisected Angle. 

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

Geometry
Problem 1516 and a Thematic Poem.
Finding the Length of a Side in an Equiangular Hexagon with Given Three Side Lengths. Difficulty Level: High School. 

Geometry
Problem 1515 and a Thematic Poem.
Mastering Triangle Distance Calculation: Find the Distance from the Intersection of Medians to an Exterior Line. Difficulty Level: High School. 

Geometry
Problem 1514 and a Thematic Poem.
Discover the Secret to Finding Distances in Regular Hexagons with Interior Squares. Difficulty Level: High School. 

Geometry
Problem 1513 and a Thematic Poem.
Solving the base in a Right Trapezoid with Double Angle and Sum of Two
Sides. Difficulty Level: High School. 

Geometry
Problem 1512 and a Thematic Poem.
Finding the Length of a Segment in a Triangle with a Median and a Cevian with Given Ratio. Difficulty Level: High School. 

Geometry
Problem 1511 and a Thematic Poem.
Post a solution Finding the Altitude of an Isosceles Triangle Using Distances from a Point on the Extension of the Base. Difficulty Level: High School. 

Geometry
Problem 1510 and a Thematic Poem.
Congruence of Triangles, Perimeter, Measurement. Difficulty Level: High School. 

Geometry
Problem 1509 and Thematic Poem.
Congruence of Triangles in a Trapezoid and a Square, Measurement. Difficulty Level: High School. 

Geometry
Problem 1508.
Understanding Triangle Geometry: Isosceles, Equilateral, Quadrilateral, Angular. Difficulty Level: High School. 

Geometry
Problem 1507.
Understanding Triangle Geometry: Double Angles, Altitudes, and Measurements. Difficulty Level: High School. 

Geometry
Problem 1504.
Squares, Equilateral Triangle, Parallel, Angle. 

Geometry
Problem 1503.
Triangle, Incircle, Tangent, Congruence, Perpendicular. 

Geometry
Problem 1502.
Right Triangle, Incircle, Inradius, Geometric Mean of 2 Inradii, Angle Bisector, Perpendicular, Tangential Quadrilateral. 

Geometry
Problem 1500.
Circle, Perpendicular, Tangent, Secant, Cyclic Quadrilateral, Parallel, Similarity, Measurement. 

Geometry
Problem 1499.
Triangle, Angles, Cevian, Congruence, Isosceles, Equilateral, Auxiliary Construction. 

Geometry
Problem 1497.
Triangle, Transversal, Same Ratio, Proportionality, Isosceles, Double Angle. 

Geometry
Problem 1496.
Triangle, Congruence, Isosceles, Double Angle, 30 Degrees. 

Geometry
Problem 1492.
Right Triangle, Altitude, Incenters, Angle, Measurement. 

Geometry
Problem 1491.
Cyclic Quadrilateral, Diagonal, Incircle, Angle, Measurement. 

Geometry
Problem 1490.
Triangle, Cevian, Incircle, Tangent, Measurement. 

Geometry
Problem 1489.
Right Triangle, Angle Bisectors, Perpendicular, Measurement. 

Geometry
Problem 1488.
Right Triangle, Altitude, Incircle, Tangent, Measurement. 

Geometry
Problem 1487.
Right Triangle, Altitude, Incircle, Tangent, Measurement. 

Geometry
Problem 1486.
Right Triangle, Altitude, Incircle, Tangent, Measurement. 

Geometry
Problem 1485.
Triangle, Orthocenter, Altitude, Circle, Diameter, Tangent, Measurement. 

Dynamic Geometry 1480.
Japanese Theorem for Cyclic Polygon, Sangaku, Triangulation, Nonintersecting Diagonals, Sum of Inradii, Invariant, Stepbystep Illustration. GeoGebra,
iPad. 

Dynamic Geometry 1479.
Triangle, Circumcircle, Angle Bisector,
Perpendicular Bisector, Chord, Concyclic Points, Parallel Lines,, Stepbystep Illustration. GeoGebra,
iPad. 

Dynamic Geometry 1478.
Cyclocevian, ReuschleTerquem Theorem, Concurrent Cevians, Triangle, Circumcircle, Secant line, Stepbystep Illustration. GeoGebra,
iPad. 

Dynamic Geometry 1477.
Miquel's Pentagram Theorem, Pentagon, Triangle, Circumcircles, Concyclic Points, Stepbystep Illustration. GeoGebra,
iPad. 

Dynamic Geometry 1476.
DrozFarny Line Theorem, Triangle, Orthocenter, Perpendicular, Collinear Midpoints, Stepbystep Illustration. GeoGebra,
iPad. 

Dynamic Geometry 1474.
Butterfly Theorem, Circle, Chords, Midpoints, Stepbystep Illustration. 

Dynamic Geometry 1473.
Kosnita's Theorem, Triangle, Four Circumcenters, Concurrent Line, Stepbystep Illustration. 

Dynamic Geometry 1472.
Cyclic Quadrilateral, Perpendicular Diagonals, Rectangle, Stepbystep Illustration. 

Dynamic Geometry 1471.
Equilateral Triangle, Inside/Outside Point, Incenters, Tangency Points, Concurrent Lines, Stepbystep Illustration. 

Dynamic Geometry 1470.
Tangential Quadrilateral, Incircles, Tangent,
Parallel, Rhombus, Stepbystep Illustration. 

Dynamic Geometry 1469.
Triangle, Circumradius, Inradius, Midpoints, Arcs, Sum of Distances, Stepbystep Illustration. 

Dynamic Geometry 1468.
Steiner's Theorem, Triangle, Circumradius, Inradius, Sum of Exradii, Stepbystep Illustration. 

Geometry Problem 1467.
Square, Rectangle, Triangle, Area. 

Geometry Problem 1465.
Tangential Quadrilateral, Incenter, Inscribed Circle, Equal Sum of Areas.
Stepbystep Illustration using GeoGebra. 

Geometry Problem 1464.
Quadrilateral, Interior Point, Midpoint of Sides, Equal Sum of Areas.
Stepbystep Illustration using GeoGebra. 

Geometry Problem 1463.
Parallelogram, Interior Point, Opposite Triangles with Equal Sum of Areas.
Stepbystep Illustration using GeoGebra. 