(02.04 MC) Below is a two-column proof incorrectly proving that the three angles of ΔPQR add up to 180°:   Statements Reasons Draw line ZY parallel to Construction m∠ZRP + m∠PRQ + m∠QRY = m∠ZRY Angle Addition Postulate ∠ZRP ≅ ∠RPQ Alternate Interior Angles Theorem ∠QRY ≅ ∠PQR Alternate Interior Angles Theorem m∠RPQ + m∠PRQ + m∠PQR = m∠ZRY Substitution m∠ZRY = 180° Definition of Supplementary Angles m∠RPQ + m∠PRQ + m∠PQR = 180° Substitution Which statement will accurately correct the two-column proof?

(03.02 MC) Decide whether the triangles are similar. If so, determine the appropriate expression to solve for x.

(02.03 MC) Triangle ABC has been translated to create triangle A′B′C′. Angles C and C′ are both 32 degrees, angles B and B′ are both 72 degrees, and sides BC and B′C′ are both 5 units long. Which postulate below would prove the two triangles are congruent?

(01.03 MC) Which step is the same when constructing an inscribed square and an inscribed regular hexagon?

(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?

(02.06 MC) Figure ABCD is a rhombus, and m∠AEB = 7x + 6. Solve for x.

(02.04 MC) Tamara is writing statements to prove that the sum of the measures of interior angles of triangle PQR is equal to 180°. Line m is parallel to line n. Which is a true statement she could write?

(01.03 MC) Which step is the same when constructing an inscribed square and an inscribed equilateral triangle?

(01.03 LC) What is a necessary step for constructing parallel lines?