Geometry Competency Assessment

A triangle has vertices A(1, 2), B(3, 6), and C(5, 2). Describe a sequence of rigid motions that maps this triangle onto a congruent triangle located in the third quadrant. Explain how the rigid motions preserve congruency.

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Which of the following justifies the conclusion that two triangles are congruent based on the information provided?

• Two pairs of angles and one pair of non-included sides are congruent

• Two pairs of sides and one pair of included angles are congruent

• Three pairs of sides are congruent

• Two pairs of sides and one non-included angle are congruent

Given quadrilateral PQRS with vertices at P(1, 2), Q(4, 6), R(7, 2), and S(4, -2), determine whether PQRS is a rhombus. Justify your answer using coordinate geometry.

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Which transformation or sequence of transformations always produces a figure similar to the original?

• Translation

• Reflection

• Dilation

• Rotation

Given a circle with center O and a radius of 5 units, a chord AB is 6 units long. Calculate the perpendicular distance from O to chord AB.

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A trapezoid has bases of 10 cm and 14 cm, and a height of 6 cm. What is the area of the trapezoid?

• 72 cm²

• 144 cm²

• 48 cm²

• 84 cm²

A ladder leans against a vertical wall, forming a 65° angle with the ground. If the foot of the ladder is 6 feet from the wall, how tall is the ladder? Round your answer to the nearest tenth.

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• Four times total

• Fives times total

• Two times total

• Six times total

Which right triangle lengths show incorrect values for a, b, and c according to the Pythagorean Theorem?

• Triangle A:

  a = 8 , b = 15, c=17

• Triangle B:

  a = 3, b = 4, c = 5

• Triangle C:

  a = 8, b = 9, c = 10

• Triangle D:

  a = 6, b = 8, c = 10

Solve for x. Explain how you would do each step.

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