Congruent and Similar Triangles

Congruent and Similar Triangles: Level 2 Challenges


\(\overline{AB} \) is parallel to \(\overline{DE} \), \(AC=5,\) and \(CD=13.\)

If the area of \(\triangle ABC\) is \(11,\) what is the area of \(\triangle CDE\) ?

In the right triangle above, a height is drawn to the hypotenuse. Find \(x+y+z.\)

In the above diagram, \(\square ABCD\) is a square with side \(\overline{AD}\) extended to point \(E\), and \(\overline{BE}\) is a straight line. If the length of \(\overline{BC}\) is \(\lvert \overline{BC}\rvert = a=30\) and \(\lvert \overline{CF}\rvert =b= 20,\) what is the area of \(\triangle CEF?\)

The area of the red triangle is 25 and the area of the orange triangle is 49. What is the area of the trapezium \(ABCD?\)

The figure shows an isosceles \( \triangle ABC \) with \( AB = BC \). The line \( DE \) cuts \( AC \) extended at \( F \). If \( AD = 5, CE = 3, \) and \( EF = 8, \) find \( DE \).


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