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.
![Geometry Problem 1507: Understanding Triangle Geometry: Double Angles, Altitudes, and Measurements. Difficulty Level: High School](p1507-discover-isosceles-triangle-doble-angle-measurement-altitude-perpendicular.png)
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.
- Suggestions:
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.
Discover Even More: See Also...
Problem 1508
![Geometry Problem 1508: Understanding Triangle Geometry: Isosceles, Equilateral, Quadrilateral, Angular. Difficulty Level: High School](p1508-isosceles-equilateral-triangle-angles-quadrilateral-60-80-degrees.png)
Problem 1506
![Geometry Problem 1506: Parallel Rays, Angles. Difficulty Level: High School.](p1506-two-parallel-lines-angles-corresponding-alternate.png)
Problem 1505
![Geometry Problem 1505: Three rays, Angles, Angle Bisector](p1505-three-parallel-rays-angles-corresponding-alternate-consecutive-bisector.png)
Problem 1504
![Geometry Problem 1504: Squares, Equilateral Triangle, Parallel, Angle](p1504-3-squares-equilateral-triangle-angle-parallel.png)
Problem 1503
![Triangle, Incircle, Tangent, Congruence, Perpendicular](p1503-triangle-transversal-line-tangent-incircle-distance-vertices-perpendicular-congruence.gif)
Problem 1502
![Right Triangle, Incircle, Inradius, Geometric Mean of 2 Inradii, Angle Bisector, Perpendicular](p1502-rigth-triangle-incircles-measurement-inradius-square-quadrilateral.gif)
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