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(01.02 LC) Which of these is a correct step in constructing an angle bisector?

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

(01.06 MC) Kyle is creating a frame for a model car. He begins by piecing two rods together, as shown in the diagram. Justify why ∠AEC is a right angle.

(01.06 LC) Angles BAE and FAC are straight angles. What angle relationship best describes angles BAC and EAF?

(01.03 MC) Natalie is completing construction of an equilateral triangle inscribed in a circle, as shown below: What should be the next step in her construction?

(01.03 MC) Jaira is completing construction of a regular hexagon inscribed in a circle, as shown below: What should be the next step in her construction?

(01.02 MC) Ben uses a compass and a straightedge to bisect angle PQR, as shown below: Which statement best explains why Ben uses the same width to draw arcs from A and B that intersect at S?

(01.03 LC) What is a necessary step for constructing perpendicular lines through a point off the line?

(01.02 MC) Ben uses a compass and straightedge to bisect , as shown: Which statement best explains why Ben must open the compass to a width greater than half of ?

(01.07 MC) Fill in the missing statement and reason in the proof of the corresponding angles theorem. It is given that is parallel to and points E, G, H, and F are collinear. The measure of ∠EGF is 180°, by the definition of a straight angle. ∠AGE and ∠AGF are adjacent, so the measure of ∠AGE plus the measure of ∠AGF equals the measure of ∠EGF, by the Angle Addition Postulate. Then, substituting for the measure of ∠EGF it can be said that the measure of ∠AGE plus the measure of ∠AGF equals 180°. ________, so the measure of ∠CHE plus the measure of ∠AGF equals 180°. Substituting once again means that the measure of ∠AGE plus the measure of ∠AGF equals the measure of ∠CHE plus the measure of ∠AGF. The measure of ∠AGE is equal to the measure of ∠CHE ________. Finally, by the definition of congruence, ∠AGE is congruent to ∠CHE.