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Isosceles Triangle, Theorems and Problems - Table of Content 1

Isosceles Triangle IndexSome key concepts to keep in mind when solving problems involving isosceles triangles in geometry include:

  1. Definition: An isosceles triangle is a triangle that has two sides of equal length and two angles of equal measure.

  2. Base angles: The two angles opposite the equal sides of an isosceles triangle are called the base angles. They are always equal in measure.

  3. Altitude: The altitude of an isosceles triangle is a line segment that is perpendicular to the base and intersects the opposite vertex. The altitude also bisects the base into two equal segments.

  4. Isosceles triangle theorem: This theorem states that if two sides of a triangle are equal, then the angles opposite those sides are also equal.

  5. In an isosceles triangle the exterior angle opposite to the base is equal in measure to twice the base angle.

  6. Triangle sum theorem: This theorem states that the sum of the angles in a triangle is always 180 degrees.

When solving problems involving isosceles triangles, it can be helpful to use these concepts to identify relationships between angles and sides, and to apply the appropriate theorem or formula to find missing measures.

Geometry Problem 1561

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

Geometry Problem 1557

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

Geometry Problem 1554

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

Geometry Problem 1550

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

Geometry Problem 1544

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

Geometry Problem 1539

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

Geometry Problem 1529

Geometry Problem 1529: Unlock the Mystery of Triangles: Solving for the Missing Angle with 100-50-30 Degree Angles and Cevian Lengths - A High School Challenge.
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Geometry Problem 1528

Geometry Problem 1528: Cracking the Circle Code: Unveiling the Tangent and Angle of an Inscribed Circle within a 90-Degree Circular Sector.
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Geometry Problem 1525

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

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

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 1513

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 1511

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

Geometry Problem 1508

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

Geometry Problem 1498

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

Geometry Problem 1497

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

Geometry Problem 1496

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

Geometry Problem 1488

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

Geometry Problem 1487

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

Dynamic Geometry 1483

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

Problem 1415

Geometry Problem 1415.
Right Triangle, Altitude, Incircle, Excircle, Tangency Points, Isosceles Triangle.

Problem 1414

Geometry Problem 1414.
Right Triangle, Altitude, Incircle, Excircle, Tangency Points, Isosceles Triangle.

Problem 1413

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

Problem 1411

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

Problem 1401

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

Problem 1398

Geometry Problem 1398.
Isosceles Triangle, Circle, Radius, Perpendicular, Measurement.

Problem 1387 Quadrilateral, Double Angle, Congruence, Isosceles Triangle

Geometry Problem 1387.
Quadrilateral, Double Angle, Congruence, Isosceles Triangle.

Problem 1386 Thabit ibn Qurra Theorem,Pythagorean Theorem to any triangle

Geometry Problem 1386.
Thabit ibn Qurra (826 -901) Theorem and more conclusions, generalized Pythagorean Theorem to any triangle.

Problem 1377 Isosceles Triangle, Circle

Geometry Problem 1377.
Isosceles Triangle, Interior Cevian, Equal Sum of Exradii, Excircle.

Problem 1376 Isosceles Triangle, Circle

Geometry Problem 1376.
Isosceles Triangle, Interior Cevian, Excircles, Tangency Points, Parallel Lines.

Problem 1375 Isosceles Triangle, Circle

Geometry Problem 1375.
Isosceles Triangle, Interior Cevian, Exradius, Excircle, Altitude to the Base.

Problem 1374 Isosceles Triangle, Circle

Geometry Problem 1374.
Isosceles Triangle, Exterior Cevian, Incircle, Excircle, Tangency Points, Parallel Lines.

Problem 1373 Isosceles Triangle, Altitude

Geometry Problem 1373.
Isosceles Triangle, Exterior Cevian, Inradius, Exradius, Altitude to the Base.

Geometry problem 1341

Problem 1341.
Geometry Problem 1341: Isosceles Triangle, 80-20-80 Degrees, Circumcenter, Angle Bisector.

Geometry problem 1340

Problem 1340.
Triangle, Incenter, Concentric Circles, Isosceles Triangles, Congruence.

Geometry problem 1324

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

Geometry problem 1287

Geometry Problem 1287.
Triangle, 40-100-40 Degrees, Congruence, Area, Metric Relations, Measurement.

Geometry problem 1280

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

Geometry problem 1274

Geometry Problem 1274.
Isosceles Triangle, 80-20-80 Degrees, Area, Inradius, Circumradius, Angle Bisector, Metric Relations, Measurement.

Geometry problem 1272

Geometry Problem 1272.
Isosceles Triangle, Median, Midpoint, Perpendicular, 90 Degrees, Angles, Congruence.

Geometry problem 1262

Geometry Problem 1262.
Isosceles Triangle, Altitude, Medians, 90 Degrees, Perpendicular.

Geometry problem 1149

Geometry Problem 1149.
Isosceles Triangle, Altitude, Cevian, Incircles, Tangent, Congruence.

Geometry problem 1129

Geometry Problem 1129.
Isosceles Triangle, Circumcenter, Incenter, Parallel Lines, Perpendicular Lines.

Geometry Problem 1120

Geometry Problem 1120.
Isosceles Right Triangle, 120 Degree, Angle, Equilateral, Metric Relations.

Geometry Problem 1114

Geometry Problem 1114.
Right Triangle, Angle Trisection, Isosceles, Congruence.

Geometry Problem 1075

Geometry Problem 1075.
Quadrilateral, Right Triangle, 90 Degrees, Isosceles, Midpoint, Distance.

Geometry Problem 1042

Geometry Problem 1042.
Scalene Triangle, Isosceles, Equal Angles, Parallelogram, Congruence.

Geometry Problem 1040

Geometry Problem 1040.
Isosceles Triangle, Transversal Line, Metric Relations.

Geometry Problem 1039

Geometry Problem 1039.
Isosceles Triangle, Circle, Tangent Line, Parallel Line.

Geometry Problem 1038

Geometry Problem 1038.
Isosceles Triangle, Angle, 80, 20, 25, 65 Degrees.

Geometry Problem 1000

Geometry Problem 1000.
Scalene Triangle, Isosceles, Angle, 120 Degree, Midpoint, Distance, Equilateral, Congruence, Perpendicular, Metric Relations.

Geometry Problem 998

Geometry Problem 998.
Scalene Triangle, Isosceles, Angle, 120 Degree, Midpoint, Equilateral, Congruence.

Geometry Problem 991

Geometry Problem 991.
Triangle, Incircle, Tangency Points, Isosceles, Midpoint, Collinearity, Congruence, Circle.

Geometry Problem 958

Geometry Problem 958.
Isosceles Triangle, Altitude, 45 Degrees, Perpendicular, Angle Bisector, Metric Relations.

Problem 886

Geometry Problem 886
Right Triangle, Incenter, Angle Bisector, Perpendicular, 45 Degrees, Concyclic Points, Isosceles Right Triangle. GeoGebra, HTML5 Animation for Tablets (iPad, Nexus).

Geometry Problem 874

Geometry Problem 874
Isosceles Triangle, Circumcircle, Circumcenter, Congruence.

Geometry problem 867, Isosceles Triangle, Median, Perpendicular, Angle, Congruence

Geometry Problem 867
Isosceles Triangle, Median, Perpendicular, Angle, Congruence.

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

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

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Last updated: Feb 18, 2024