Trigonometry : Triangles

Study concepts, example questions & explanations for Trigonometry

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Example Questions

Example Question #9 : Use Special Triangles To Make Deductions

In the figure below,  is a diagonal of quadrilateral .  has a length of is congruent to .

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Which of the following is a true statement?

Possible Answers:

The area of quadrilateral  is .

The area of quadrilateral  is .

The perimeter of quadrilateral  is .

The perimeter of quadrilateral  is .

Correct answer:

The area of quadrilateral  is .

Explanation:

Since  and  are perpendicular,  is a right angle. Since no triangle can have more than one right angle, and  is isosceles,  must be congruent to . Since angle CBD is congruent to  and  measures 90 degrees,  and  can be calculated as follows:

Therefore,  and  are both equal to 45 degrees.  is a 45-45-90 triangle. Therefore, the ratio between side lengths and hypotenuse  is . Anyone of the four side lengths of quadrilateral  must, therefore, be equal to . To find the area of , multiply two side lengths: .

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