Geometry Content Vocab Practice ProblemsBelow you will find a list of action words that appear throughout the GSE Geometry standards. For each word, an action item (question) has been provided for you to complete. Review the assignment below in order to practice problem solving using the content and vocab that will be required of you on the EOC.

“Apply”

MGSE9-12.S.CP.7 – Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B), and interpret the answers in context.

Kyle draws one card from a standard deck of 52 cards. What is the probability that he draws an 8 or a diamond?

A . 14

B . 113

C . 413

D . 1752

“Derive”

MGSE9-12.G.GPE.1 – Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by and equation.

Which equations describes a circle with center (4, -7) and radius 9?

A .(x−4)2+( y+7)2=81

B .(x+4)2+( y+7)2=81

C .(x−4)2+( y+7)2=9

D .(x−4)2+( y+7)2=9

“Prove”

MGSE9-12.G.CO.9 Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints.

In the figure below, angles 1,2,3,and 4 are created by the intersection of line n with parallel lines l and m.

The table shows the second column of a 2-column proof used to prove that the interior angles, formed by the intersection of a transversal and two parallel lines and on the same side of the transversal, are supplementary.

Place the statements in order to match the reasons of the proof.

a.∠1≅∠3

b. ∠1≅∠2

c.∠3 is supplementary ¿∠ 4

d. ∠1is supplementary ¿∠4

e.Linesl∧mare∥¿

f.∠2≅∠3

“Construct”

MGSE9-12.G.C.3 Construct the inscribed and circumscribed circles of a triangle.

Carmen wants to construct a circle to be circumscribed about triangle PQR. Which point should she use for the center of the circle?

A. The point where the perpendicular bisectors of two sides of the triangle intersect.

B. The point where the bisectors of two angles of the triangle intersectC. The point where the medians of two sides of the triangle intersectD. The point equidistant from all three sides of the triangle.

“Use”

MGSE9-12.G.CO.6 Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.

Triangle ABC is rotated 180⁰ clockwise about the origin to form triangle A’B’C’. Which statement can be used to explain why triangle A’B’C’ is congruent to triangle ABC?

A . A ' B'=AB=5 ; B'C '=BC=3 ;∧A 'C '=AC=√34

B . A 'B '=AB=3 ;B'C'=BC=5 ;∧A 'C'=AC=√17

C . A' B'=BC=5 ;B'C'=CA=3 ;∧A 'C '=BC=√34

D . A 'B'=BC=5 ; B'C '=CA=3;∧A'C'=BC=√17

“Explain”

MGSE9-12.G.GMD.2 Give an informal argument using Cavalieri’s principle for the formulas for the volume of a sphere and other solid figures.

The leaning tower of Pisa no longer stands vertically. It is approximately 55.67 meters tall, and its diameter is approximately 15.484 meters.

A. Estimate the volume of the tower. Show your work.B. Explain, using Cavalieri’s principle, why the approach used to estimate the

volume in part A is appropriate.

“Understand”

MGSE9-12.S.CP.2 Understand that if two events A and B are independent, the probability of A and B occurring together is the product of their probabilities, and that if the probability of two events A and B occurring together is the product of their probabilities, the two events are independent.

A catch-and-release fisherman catches a fish and then releases the fish back into the river so as not to harm the fish.

At a local river, 50% of the fish are white sturgeon, 35% are brook trout, and 15% are Chinook salmon.

If a fisherman catches and releases a fish and then catches and releases a second fish, then what is the probability that both fish he caught were white sturgeon? Give your answer as a decimal rounded to the nearest hundredth.

Solutions and Rationales

Apply

Derive

Prove

Construct

Use

Explain

Understand