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Geometry

Properties of Triangles

Triangles Problem Solving

         

As shown in the above diagram, Raj folds a rectangular paper \(ABCD\) in such a way that side \(BC\) becomes \(BE.\) If the length of \(\overline{AB}\) is \(3\) and the length of \(\overline{BC}\) is \(15,\) what is the area of \(\triangle ABF?\)

Note: The above diagram is not drawn to scale.

In the above diagram, we are given \[\angle BAC=90^\circ, \angle ACD=75^\circ, \angle CBD=75^\circ, \angle BDE=110^\circ.\] What is \(\angle ABC\) in degrees?

In right triangle \(ABC\), we are given that \(\angle ABC = 90^\circ\) and \(AC= 34\). \(D\) is a point on line segment \(BC\) such that \(BD=12, DC=18\). What is the length of \(AD\)?

In the above diagram, the ratio of the length of \(\overline{AD}\) to the length of \(\overline{DC}\) is \(3:2.\) If the area of \(\triangle ABE\) is \(13,\) what is the area of \(\triangle BEC ?\)

Note: The above diagram is not drawn to scale.

In triangle \(ABC\), we have \(AB = 47, BC = 48, CA = 49 \). Points \(D, E,\) and \(F\) are the midpoints of \(BC, CA,\) and \(AB\) respectively. What is the perimeter of triangle \(DEF\)?

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