Geometry EOC Review: Day 1

Rewrite the following definition as a biconditional statement. Definition: The midpoint of a segment is the point that divides the segment into two congruent segments.

• If a point is not the midpoint of a segment, then the point doesn’t divide the segment into two congruent segments.

• A point is the midpoint of a segment if and only if the point divides the segment into two congruent segments.

• If a point divides the segment into two congruent segments, then the point is the midpoint.

• A point divides the segment into two congruent segments if and only if the point is the midpoint.

Tags

CCSS.HSG.CO.C.10

What is the inverse of the statement, “If a parallelogram has a right angle, then the parallelogram is a rectangle”?

• If a parallelogram is a rectangle, then the parallelogram has a right angle.

• If a parallelogram is not a rectangle, then the parallelogram does not have right angle.

• If a parallelogram does not have a right angle, then the parallelogram is not a rectangle.

• If a parallelogram has a right angle, then the parallelogram is not a rectangle.

Tags

CCSS.HSG.CO.C.11

What is the converse of the statement, “If two angles are congruent, then they have the same measure”?

• If two angles are not congruent, then they have the same measure.

• If two angles are not congruent, then they don’t have the same measure.

• If two angles have the same measure, then they are congruent.

• If two angles don’t have the same measure, then they are not congruent.

Tags

CCSS.8.G.A.2

The Triangle Midsegment Theorem states: "If a segment joins the midpoints of two sides of a triangle, then it is parallel to the third side and half its length." Which of the following represents the converse of this theorem?

• If a segment is parallel to the third side of a triangle and is half its length, then it joins the midpoints of two sides.

• If a segment joins two midpoints of a triangle, then it is not parallel to the third side.

• If a segment is parallel to one side of a triangle, then it divides the other two sides into equal parts.

• If a segment is half the length of one side of a triangle, then it must be a midsegment.

Tags

CCSS.HSG.SRT.B.4

Which situation would provide a counterexample to this statement? "Alternate interior angles are never supplementary."

• A line that is parallel to two parallel lines.

• A transversal that forms 45° angle with two parallel lines.

• A transversal that is perpendicular two parallel lines.

• A line that has a slope that is the reciprocal of the slopes of two parallel lines.

Tags

CCSS.8.G.A.5

Which of the options best describes a counterexample to the assertion below? "If one pair of opposite sides of a quadrilateral is congruent, then the quadrilateral is a parallelogram."

• Isosceles trapezoid

• Rectangle

• Rhombus

• Square

A student claims: "If two sides of a triangle are the same length, then the third side must be shorter than either of those sides." Which of the following triangles provides a counterexample to the student’s claim? Select all that apply.

• A triangle with side lengths 2 cm, 3 cm, and 3 cm.

• A triangle with side lengths 5 cm, 4 cm, and 5 cm.

• A triangle with side lengths 6 cm, 6 cm, and 6 cm.

• A triangle with side lengths 10 cm, 7 cm, and 10 cm.

Tags

CCSS.HSG.SRT.B.5

In the diagram below of ΔABC, D and E are the midpoints of AB and AC, respectively, and DE is drawn. Which methods could be used to prove ΔABC ~ ΔADE?

I. AA similarity

II. SSS similarity

III. SAS similarity

• I only

• I and II

• II and III

• I, II, and III

Tags

CCSS.HSG.SRT.B.5

In the figure, ∠QPT and ∠STP are right angles. Sides PQ and TS are congruent. Which statement is always true?

• RS ≅ PQ

• RS ≅ RQ

• RS ≅ ST

• PS ≅ PT

Tags

CCSS.HSG.CO.C.11