Problem 101. Equilateral Triangle, Pythagoras, Angles. Level: High School, SAT Prep, College

In the figure below, given an equilateral triangle ABC, D is an interior point. If a2 = b2 +c2 prove that the measure of angle BDC is equal to 150°.
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Equilateral triangle, Pythagoras. Elearning

 

 

 

FACTS AND HINTS:

Geometry problem solving is one of the most challenging skills for students to learn. When a problem requires auxiliary construction, the difficulty of the problem increases drastically, perhaps because deciding which construction to make is an ill-structured problem. By “construction,” we mean adding geometric figures (points, lines, planes) to a problem figure that wasn’t mentioned as "given."

 USE

  • Pythagorean Theorem Converse

  • Congruence of Triangles SAS

  • The sum of the measures of the trhee angles of a triangle is 180.

 

 

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