1 Name _________________________________________ Geometry Common Core Regents Review Packet - 3 Topic 1 : Equation of a circle 1. The endpoints of a diameter of a circle are located at (5, 9) and (11,17). Which is an equation of the circle? A ( ) ( ) B ( ) ( ) C ( ) ( ) D ( ) ( ) 2.Find the equation of the circle below 3.Which equation represents circle O with center and radius 9? 1) 2) 3) 4) 4.What is the equation of a circle whose center is 4 units above the origin in the coordinate plane and whose radius is 6? 1) 2) 3) 4) 5. The coordinates of the endpoints of the diameter of a circle are and . What is the equation of the circle? 1) 2) 3) 4) 6. Identify the center and the radius of the following circle. 2 2 4 12 41 x y x y Equation with center (0,0) and radius r Equation with center (h,k) and radius r ( ) ( )
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Name _________________________________________ Geometry Common Core Regents Review Packet - 3
Topic 1 : Equation of a circle
1. The endpoints of a diameter of a circle are located at (5, 9) and (11,17). Which is an equation of the circle? A ( ) ( ) B ( ) ( ) C ( ) ( ) D ( ) ( )
2.Find the equation of the circle below
3.Which equation represents circle O with center and radius 9?
1)
2)
3)
4)
4.What is the equation of a circle whose center is 4 units above the origin in the coordinate plane and whose radius is 6? 1)
2)
3)
4)
5. The coordinates of the endpoints of the diameter of a circle are and . What is the equation of
the circle? 1)
2)
3)
4)
6. Identify the center and the radius of the following circle.
2 2 4 12 41x y x y
Equation with center (0,0) and radius r Equation with center (h,k) and radius r ( ) ( )
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Topic 2: Scale Drawings
1.The perimeter of the smaller of two similar trapezoids is 18 units. The ratio of the sides of the smaller to the larger trapezoid is 3:5. What is the perimeter of the larger trapezoid?
1) 48 2) 30 3) 10.8 4) 6.75
2.Which of the following transformations preserves angle measure, but not distance?
2. In the diagram of and , ≅ and ̅̅ ̅̅ ̅ ≅ ̅̅ ̅̅ . Prove: ̅̅ ̅̅ ̅ ≅ ̅̅ ̅̅ .
Ways to prove triangles are similar - Symbol ~ 3. Fill in the missing blanks with the correct reason for the proof.
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Topic 5: Proving Properties of Geometric Figures
Parallelogram Rectangle Rhombus Square
Opposite angles Consecutive angles supplementary Opposite sides Opposite sides parallel Diagonals bisect each other Diagonals bisect angles Diagonals to each other Diagonals Equiangular Equilateral
1. All of the following must have congruent diagonals
except a. A rectangle b. A square c. A parallelogram d. Isosceles trapezoid
2. A parallelogram must be a rhombus if the a. Diagonals are perpendicular b. Opposite angles are congruent c. Diagonals are congruent d. Opposite sides are congruent
3.If the measures of two opposite angles of a parallelogram are represented by 3x + 40 and x + 50, what is the measure of each angle of the parallelogram?
4.In parallelogram ABCD angle A can be represented by 3x + 20 and angle B can be represented by 7x – 40. Find the measure of each angle of the parallelogram.
5. In rhombus ABCD below, what is the measure of angle BDA?
6.Which statement is false?
1) All parallelograms are quadrilaterals. 2) All rectangles are parallelograms. 3) All squares are rhombuses. 4) All rectangles are squares.
7.The following represents a cyclic quadrilaterals. Find the values of all variables shown.