Geometric Challenge Problem 1621: Isosceles Triangle, 40-70 Degrees, Altitude, Segment Identity

Share your proof or solution in the comments below.
Target Audience: K-12, Honors Geometry, and College Mathematics Education.

In Problem 1621, we explore an isosceles triangle with angles 40 and 70, revealing a striking linear identity involving its altitude and side lengths: AC + AH .
Explore the full theorem and illustrated diagram by clicking the image below.

Click for additional details and full diagram.

Proposed Solution
We invite students, teachers, and math enthusiasts to share their insights. This challenge involves angle splits and auxiliary constructions unlocked via synthetic geometry.

How to contribute:
Post your step-by-step proof in the comments below. Feel free to:

• Describe the theorems applied.
• Share a link to your dynamic construction (GeoGebra, Desmos).

Be the first to submit a formal solution for this problem!

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Please use the box below to Enter your Comment or Solution. You can use plain text or provide links to your digital proofs.

Geometry Problem 1385: Triangle, Orthocenter, Circle, Circumcircle, Angle Bisector, Midpoint, Collinear Points

Geometry Problem. Post your solution in the comment box below.
Level: Mathematics Education, High School, Honors Geometry, College.

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Geometric Art: Typography, iPad

Details: Click on the figure below.

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Geometric Art: Typography, iPad

Details: Click on the figure below.

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Geometry Problem 804, Step by step Illustration
Click the figure to see the interactive illustration

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Theorem Proof by Leonardo da Vinci
This virtual version of Geoboard is an open-ended educational tool, ideal for elementary classrooms and other learning environments that use iPod Touches, iPhones, or iPads.

Click the figure below to see the illustration.

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