(02.06 MC) The figure below shows a quadrilateral ABCD. Sides AB and DC are congruent and parallel: A student wrote the following sentences to prove that quadrilateral ABCD is a parallelogram: Side AB is parallel to side DC, so the alternate interior angles, angle ABD and angle CDB, are congruent. Side AB is equal to side DC, and DB is the side common to triangles ABD and BCD. Therefore, the triangles ABD and CDB are congruent by SSS postulate. By CPCTC, angles DBC and BDA are congruent and sides AD and BC are congruent. Angle DBC and angle BDA form a pair of alternate interior angles. Therefore, AD is congruent and parallel to BC. Quadrilateral ABCD is a parallelogram because its opposite sides are equal and parallel. Which statement best describes a flaw in the student’s proof?

(01.01 LC) Which of the following terms is defined as a set of all points in a plane that are a given distance from a point?

(01.07 MC) Fill in the missing statement and reason in the proof of the Alternate Interior Angles Theorem. It is given that is parallel to and points E, G, H, and F are collinear. ∠AGF and ∠EGB are vertical and congruent by the Vertical Angles Theorem. ∠EGB and ∠EHD are congruent according to the ________. Finally, ________ by the Transitive Property of Equality.

(01.03 MC) An architect plans to draw a rectangular patio, with segment LM representing one side of the rectangle. He wants to construct a line passing through Q and parallel to side LM. He uses a straightedge and compass to complete some steps of the construction, as shown below: Which of these is likely to be his next step in constructing the parallel line?

(01.01 MC) Is the figure an example of a segment?

(02.01 MC) Triangle FIT has been reflected over the y-axis. Which of the following best describes the relationship between the y-axis and the line connecting F to F′?

(02.03 MC) John translated parallelogram ABCD using the rule (x, y) → (x + 3, y − 2). If angle A is 110° and angle B is 70°, what is the degree measurement of angle A′?

(03.01 MC) Quadrilateral ABCD is dilated by a scale factor of centered around (2, 2). Which statement is true about the dilation?

(01.06 MC) Which statement justifies why ∠ABF measures 130°? Given: angles ABD and DBC are complementary

(02.06 MC) Look at the quadrilateral shown below: Melissa writes the following proof for the theorem: If the diagonals of a quadrilateral bisect each other, the quadrilateral is a parallelogram: Melissa’s proof For triangles AOB and COD, angle 1 is equal to angle 2, as they are vertical angles. AO = OC and BO = OD because it is given that diagonals bisect each other. The ________ are congruent by SAS postulate. Similarly, triangles AOD and COB are congruent. By CPCTC, AB is equal to DC. By CPCTC, AD is equal to BC. As the opposite sides are congruent, the quadrilateral ABCD is a parallelogram. Which is the missing phrase in Melissa’s proof?