Triangles
Practice triangle properties, similarity, and the Pythagorean theorem.
27 questions
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Two nearby trees are perpendicular to the ground, which is flat. One of these trees is 10 feet tall and has a shadow that is 5 feet long. At the same time, the shadow of the other tree is 2 feet long. How tall, in feet, is the other tree?
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The length of a rectangle’s diagonal is 5√17, and the length of the rectangle’s shorter side is 5. What is the length of the rectangle’s longer side?
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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?
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The perimeter of an equilateral triangle is 624 centimeters. The height of this triangle is k√3 centimeters, where k is a constant. What is the value of k?
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For the right triangle shown, a = 4 and b = 5. Which expression represents the value of c?
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In ▵RST, the measure of ∠R is 63°. Which of the following could be the measure, in degrees, of ∠S ?
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If the measure of angle A of triangle ABC is 3x, the measure of angle B is 5x, and the measure of angle C is 4x, what is the value of x?
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If the measure of angle A of triangle ABC is 5x + 10, the measure of angle B is x + 10, and the measure of angle C is 2x, which of the following is true of triangle ABC?
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The measure of an angle exterior to angle F of triangle DEF measures 16x + 12. If angle F measures 8x, what is the measure of angle F?
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If the measures of angles A and B of triangle ABC are each 2x + 5 and the measure of angle C is 3x – 5, what is the measure of angle exterior to angle A?
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The measure of an angle exterior to angle F of triangle DEF measures 120°. Which of the following must be true?
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If the measure of angle F in triangle DEF is half the sum of the measures of angles D and E, what is the measure of an angle exterior to F?
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Triangles JKL and MNO are congruent and equilateral. If side JK measures 6x + 3 and side MN measures x 2 – 4, what is the length of side NO?
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Triangles GHI and PQR are similar and isosceles. If side HG of triangle GHI is congruent to side PQ, its corresponding side in triangle PQR, which of the following must be true?
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The bases of a right triangle measure x – 3 and x + 4. If the hypotenuse of the triangle is 2x – 3, what is the length of the hypotenuse?
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If the length of a base of right triangle DEF is 8 units and the hypotenuse of triangle DEF is 8√5 units, what is the length of the other base?
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If the lengths of the bases of right triangle GHI are 9 units and 15 units respectively, what is length of the hypotenuse of triangle GHI?
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If the longer base of triangle XYZ is three times the length of the shorter base, a, what is the length of the hypotenuse in terms of the shorter base?
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Which of the following triangles is a multiple of the triangle with sides measuring x, x – 5, and x + 5, when x is greater than 0?
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Angle T of right triangle TUV measures 45°. If base TU measures 10 units, what is the length of the hypotenuse of triangle TUV?
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The hypotenuse of an isosceles right triangle measures x units. What is the length of a base of the triangle?
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Angle Q of triangle PQR is a right angle, and side QR measures 4 units. If the sine of angle P is equal to the sine of angle R, what is the length of side PR?
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Given right triangle ABC with right angle B, angle A is twice the size of angle C. If the measure of side AB is 7 units, what is the measure of side AC?
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What is the perimeter of an isosceles right triangle whose hypotenuse is 5√2 units?
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What is the perimeter of a square with a diagonal measuring 2x√2 units?
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If the perimeter of a square is equal to 5x + 1 and the length of the diagonal of the square is (2x – 2)√2, what is the length of a side of the square?
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Angle A of rhombus ABCD measures 120°. If one side of the rhombus is 10 units, what is the length of the longer diagonal?
Hard