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The table gives the perimeters of similar triangles TUV and XYZ, where \( TU \) corresponds to \( XY \). The length of \( TU \) is 18.

What is the length of \( XY \) ?

Quadrilateral P'Q'R'S' is similar to quadrilateral PQRS, where P, Q, R, and S correspond to P', Q', R', and S', respectively. The measure of angle P is 30°, the measure of angle Q is 50°, and the measure of angle R is 70°. The length of each side of P'Q'R'S'  is 3 times the length of each corresponding side of PQRS. What is the measure of angle P '?

In triangle \( ABC \), \( AB=4,680 \)millimeters (mm) and \( BC=4,680 \)mm. Which statement is sufficient to prove that triangle \( ABC \)is equilateral?

In the figure above, \( BD \)  is parallel to \( AE \). What is the length of \( CE \)?

Right triangles LMN and PQR are similar, where L and M correspond to P and Q, respectively. Angle M has a measure of 53°. What is the measure of angle Q ?

Right triangles PQR and STU are similar, where P corresponds to S. If the measure of angle Q is 18°, what is the measure of angle S ?

In the right triangle shown, what is the value of a?

A right triangle has sides of length 4\( \sqrt{2} \), 10\( \sqrt{2} \), and \( \sqrt{232} \) units. What is the area of the triangle, in square units?

The perimeter of an isosceles right triangle is\( 94+94\sqrt{2} \)inches. What is the length, in inches, of the hypotenuse of this triangle?

The lengths of the legs of a right triangle are shown. Which of the following is closest to the length of the triangle's hypotenuse?

The perimeter of an isosceles right triangle is \( 28+28\sqrt{2} \) inches. What is the length, in inches, of the hypotenuse of this triangle?

In triangle \( ABC \), angle \( B \) is a right angle. The length of side \( AB \) is \( 10\sqrt{39} \) and the length of side \( BC \) is \( 24\sqrt{39} \). What is the length of side \( AC \)?