Geometry Problem 1507: Understanding Triangle Geometry: Double Angles, Altitudes, and Measurements. Difficulty Level: High School.
In the figure, there is a triangle ABC with altitude
AD, such that angle
B is double angle DAC. If BD measures 4 and DC measures 3, find the
measure of AB.
Definitions and Suggestions
- A triangle is a polygon that has three sides, three vertices, and three angles. Triangles are some of the most basic shapes in geometry and can be found in many different forms.
- An angle is a figure formed by two rays, or half-lines, that have a common endpoint and extend in different directions.
- An altitude of a triangle is a line segment that is drawn from a vertex of a triangle perpendicular to the opposite side or to the line containing the opposite side.
The sum of the angles in a
triangle is always 180 degrees, which is known as the Triangle Sum Theorem.
- In a triangle, if two angles are congruent, then the sides opposite those angles are also congruent.