Geometry Regents Review

CIRCLES/TRIANGLES

1

If the arc angle is 78 degrees, how many degrees is the inscribed angle that goes to that arc?

39 degrees

2

What is the circumference of a circle with radius 6? (Round to nearest tenth)

37.7

3

In a right triangle one of the sides is 9.2 cm and the Hypotenuse is 16.1 cm. Find the length of the third side. (Round to the nearest tenth) 

13.2 cm

4

Two chords intersect inside a circle. One chord is divided into segments of lengths 4 and 6. The other chord is divided into segments of lengths 3 and x. Solve for x.

x=8

5

What is the area of a sector with the degree measure of 27 degrees and the diameter is 10 meters. (Rounded to the nearest tenth)

5.9 m²

CIRCLES/TRIANGLES

1

Could {3,9,11} represent the lengths of the sides of a triangle? Explain.

Yes

2

In an isosceles triangle, one of the base angles measures 43 degrees. What is the measure of the vertex angle?

94 degrees

3

In △ABC, DE is parallel to BC. If AD = 4, DB = 6, and AE = 5, find EC?

EC=7.5

4

A 10 foot ladder leans against a garage. The base of the ladder is 6 feet from the base of the garage. How high is the garage?

8 feet

5

Mike is flying a kite at a 32 degree angle. The kites string is 20 feet long. How high up off the ground is the kite? (Round to nearest tenth)

10.6 feet

TRANSFORMATIONS

1

What are the three rigid motions?

Translation, Reflection and Rotation

2

Rule: (x, y ) --> ( x, -y );

Reflection over the x-axis

3

The image of (-3,4) under a translation is (4,0). What is the image of (5,1) under the same translation?

(12,-3)

4

If a translation maps (x,y)-> (x-2,y+3), what are the coordinates of A, the image of A'(-4,-3) after this translation?

(-2,-6)

5

What is the coordinate of the point (1,0) after a translation up 2 and down 4 and then followed by a rotation of 90 degrees counter clockwise?

(1,0) --> (3,-4) --> (4,3)

QUADRILATERALS/ VOLUME

1

What quadrilateral has both set of opposite sides are parallel and congruent, but the diagnols are not congruent?

Rhombus

2

What is the area of a triangle with a height of 5 in and base distance of 12 in?

30 in²

3

What are the 2 properties that make a parallelogram a rectangle?

1. The diagonals are congruent. 

2. There are 4 right angles.

4

Find the volume of a cylinder with diameter 6 inches and height 8 inches.

226.2 in³

5

Name the 5 properties of a parallelogram.

1. opposite sides are congruent

2. opposite sides are parallel

3. opposite angles are congruent

4. consecutive angles are supplementary

5. diagonals bisect each other

COORDINATE GEOMETRY

1

Find the midpoint of (-2,4) and (8,-2).

(3,1)

2

What is the slope between these points (2,3) and (9,5)? (Simplify the fraction)

1/3

3

Find the distance between (3,5) and (11,11)

10

4

What is the equation of a line parallel to the line y=-1/2x+1 and goes through the point (-2,4)? (In Slope Intercept Form)

y=-1/2x+3

5

What is the equation of the perpendicular bisector between the points (2,4) and (8, 12)? (In Slope Intercept Form)

y-8=-3/4(x-5)