Exam 6: Similar Triangles

In , and . If , find .

In the figure, . Also, , , and . Find TX .

In a 30°-60°-90° triangle, the hypotenuse has a length of 20 cm. Find the exact perimeter of this triangle.

What does the question mark represent in this extended proportion?

Point D lies in the interior of . Line segments are drawn from vertices A , B , and C through point D to intersect at point E , at point F , and at point G . If , , , , and , find AG . [Hint: Use Ceva's Theorem.]

Two sides of have lengths 5 inches and 6 inches. The length of the remaining and longest side is x inches. Determine all integer (whole number)values of x so that is an obtuse triangle.

In the legs of a right triangle are congruent, then the triangle is a 45°-45°-90° triangle.

Given that , the two triangles are similar. Which side of corresponds to side of the second triangle?

If and , which method is used to prove that ?

In , . Also, . Find .

If and are divided proportionally at points M and N (as shown), then .

The triple (20,21,29)is a Pythagorean Triple.

In an equilateral triangle, each side measures 12 cm. Find the length of the altitude of this triangle.

Given that , , and in , it follows that .

If in , then .

In the figure, and . What method allows you to conclude that ?

In the figure, intersects two sides of as shown. If , what relationship must hold true?

Given that , what angle of is congruent to of ?

In the figure, . If , , , and , find the value of x .

In isosceles triangle RST , . If , find the length of .