Geometry EOC Review 1

Which of the following is the contrapositive of the statement "If I can run a 5K race in under 27 minutes, then I can start the race at the front of the pack"?

• If I cannot run a 5K race in under 27 minutes, then I can start the race at the front of the pack.

• If I cannot run a 5K race in under 27 minutes, then I cannot start the race at the front of the pack.

• If I can run a 5K race in under 27 minutes, then I cannot start the race at the front of the pack.

• If I cannot start the race at the front of the pack, then I cannot run a 5K race in under 27 minutes.

• If I can start the race at the front of the pack, then I can run a 5K race in under 27 minutes.

Which of the following is the inverse of the statement "If I can run a 5K race in under 27 minutes, then I can start the race at the front of the pack"?

• If I cannot run a 5K race in under 27 minutes, then I can start the race at the front of the pack.

• If I cannot run a 5K race in under 27 minutes, then I cannot start the race at the front of the pack.

• If I can run a 5K race in under 27 minutes, then I cannot start the race at the front of the pack.

• If I cannot start the race at the front of the pack, then I cannot run a 5K race in under 27 minutes.

• If I can start the race at the front of the pack, then I can run a 5K race in under 27 minutes.

Which of the following is the converse of the statement "If I can run a 5K race in under 27 minutes, then I can start the race at the front of the pack"?

• If I cannot run a 5K race in under 27 minutes, then I can start the race at the front of the pack.

• If I cannot run a 5K race in under 27 minutes, then I cannot start the race at the front of the pack.

• If I can run a 5K race in under 27 minutes, then I cannot start the race at the front of the pack.

• If I cannot start the race at the front of the pack, then I cannot run a 5K race in under 27 minutes.

• If I can start the race at the front of the pack, then I can run a 5K race in under 27 minutes.

Write an "if...then" statement that can be written from the given statement: "A triangle is an equilateral triangle if and only if the triangle has three congruent sides."

Select the correct converse of the conditional statement written using the statement from the previous question: A triangle is an equilateral triangle if and only if the triangle has three congruent sides.

• If the triangle is equilateral then it has three congruent sides.

• If the triangle has three congruent sides then it is equilateral.

• A triangle is equilateral only when it has three congruent sides.

• Both statements are equivalent.

Which of the following statements is true?

• If a quadrilateral is a square, then it is a rectangle.

• All trapezoids are parallelograms.

• Any quadrilateral can be inscribed in a circle.

A(n)​ (a)   is a counterexample to the statement "All trapezoids are parallelograms."

• rhombus
• isosceles trapezoid
• square
• rectangle

Fill in the blank for the counterexample to the statement "Any quadrilateral can be inscribed in a circle."

Counterexample: If the quadrilateral has ________ ______ that do not equal 180⁰, then it cannot be inscribed in a circle.

Line l and AB form 90° and the point of intersection, M, is the midpoint of AB. Suppose point P lies on line l as shown below. What conjecture can be made about point P?

• Point P is closest to point A.

• Point P is closest to point B.

• Point P is equidistant to point A and point B.

• Point P is equidistant to point A, point, B, and point M.

Line l and AB form 90° and the point of intersection, M, is the midpoint of AB. Suppose another point, Q, was added to line l? What conjecture can be made about point Q?

• Point Q is closest to point A.

• Point Q is closest to point B.

• Point Q is equidistant to point A and point B.

• Point Q is equidistant to point A, point, B, and point M.