Name Geometry Common Core Regents Review Packet - 3 Topic 1 : Equation of a circle Equation with center (0,0) and radius r Equation with center (h,k) and radius r ( ) ( ) 1. The endpoints of a diameter of a circle are located at (5, 9) and (11,17). Which is an equation of the circle? ( ) ( ) ( ) ( ) 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 x y 4x 12y 41 1
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 Topic 2: Scale Drawings 2.Which of the following transformations preserves angle measure, but not distance? 1) Dilation 3) Reflection 2) Rotation 4) Translation 3. In the figure below, is parallel to and NQ=4cm, OP= 6cm, and MQ=8cm. If NO=2, how long is? 1) 10 cm 2) 2 cm 3) 6 cm 4) 4 cm 4. Triangle C is similar to triangle DEF. Which is the correct statement for the ratio of their corresponding sides? 1) C C DE DF EF 2) 3) 4) C C DF DE EF C C DE EF DF C C EF DF DE 5. In the following diagram,. If EC 3and D 1 (D), what is the length of C? 2 1) 6 2) 9 3) 12 4) 15 6. Which similarity transformation maps C onto C? a) Dilation by factor of 2 and a Rotation about the point (0, 1) b) Reflection over the origin and a Dilation by factor of 2 c) Rotation of 180 and a reflection over the line y=x d) Translation (x+2, y+5) and a dilation of 2 2
7. Determine the scale factor of the given dilation from point O? 1) 2/3 2) 2/5 3) 3/2 4) 5/2 ' O 2 cm C' 3 cm C *8. Which one of the following linear functions would remain unchanged under a dilation of 3 about the point (0, 3)? 1) y 2x 2) y 2x 3 3) y 3x 5 0 4) y x 3 9. Given C and its image ' ' C ' after a dilation with center at the origin. a) Determine the constant of dilation and the ratio of : b) re these triangles congruent, similar or neither? Explain. c) Find the ratio of the perimeter of to. d) Find the ratio of the area of to 10. Using the diagram (to the right) of the two similar triangles: a. What is the relationship between the sides of to the sides of b. Find the perimeters of both triangles. What is the relationship between the perimeter of to the perimeter of c. Find the area of both triangles. What is the relationship between the area of to the area of 11. In the diagram below, XYZ is the result of a dilation of UVW. a) Find the values of and. b) Find the ratio of the sides. c) Find the ratio of the perimeters. d)find the ratio of the areas. 3
Topic 3 : Unknown ngles Complementary ngles: Two angles that add to 90 o Supplementary ngles: Two angles that add to 180 o djacent ngles: Two angles that share a common vertex and common side. 1.Find the measure of each labeled angle. Give a reason for your solution 2.Find the measures of angles a, b, c, d, and e. 3.In the diagram below of quadrilateral CD with diagonal D, determine if is parallel to DC if m 93, m D 43, Explain your reasoning. 4.In the diagram below of triangle HQP, side HP is extended through P to T. a) Find b) Classify triangle PQH. 4
Topic 4: Proofs/Congruence Triangle Proofs Summary List the 5 ways of proving triangles congruent: 1. SS @ SS 2. SSS @ SSS 3. S @ S 4. S @ S 5. HL @ HL Which two sets of criteria CNNOT be used to probe triangles congruent. 1. @ 2. SS @ SS In order to prove a pair of corresponding sides or angles are congruent, what must you do first? Show the triangles are congruent first! Property Meaning Geometry Example Reflexive Property Transitive Property Symmetric Property ddition Property of Equality Subtraction Property of Equality Multiplication Property of Equality Division Property of Equality Substitution Property of Equality Partition Property (includes ngle ddition Postulate, Segments add, etweenness of Points, etc.) quantity is equal to itself. If two quantities are equal to the same quantity, then they are equal to each other. If a quantity is equal to a second quantity, then the second quantity is equal to the first. If equal quantities are added to equal quantities, then the sums are equal. If equal quantities are subtracted from equal quantities, the differences are equal. If equal quantities are multiplied by equal quantities, then the products are equal. If equal quantities are divided by equal quantities, then the quotients are equal. quantity may be substituted for its equal. whole is equal to the sum of its parts. If and, then. If then. If and, then. If and, then. If then ( ) ( ). If then. If, and then. If point is on, then. Statements of Equality Picture Given Statement Reason 1. C CD <D and <DC Perpendicular Lines form right are right angles ngles <D <DC ll right < s are D 5
2. EF intersects GH at J <EJH <GJF Intersecting lines form H vertical < s E J G F 3 H EF bisects GH GJ JH isector cuts segment in 1/2 E J F G 4. D bisects <C <D <DC isector cuts angle in 1/2 D C 5. M is the midpoint of M M midpoint cuts segment in 1/2 M 6. C is a straight line <D & <CD are supplementary Linear Pairs are supplementary D Picture Given Statement Reason 7. M LMN is isosceles LN is the base ML MN <MLN <MNL Isosceles 2 sides are congruent and base angles are congruent L L N 8. M LM MN <MLN <MNL When 2 sides are congruent the angles opposite those sides are also congruent N 9. <1 <1 Reflexive Converse also true if two angles are the sides opposite them are congruent 1 C 10. CD EF CD C D E F EF Transitive 6
1. For each pair of triangles, tell which triangles can be proven congruent (if at all) and by what method. C D ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 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. 7
Opposite angles Consecutive angles supplementary Opposite sides Opposite sides parallel Diagonals bisect each other Diagonals bisect angles Diagonals to each other Diagonals Equiangular Equilateral Topic 5: Proving Properties of Geometric Figures Parallelogram Rectangle Rhombus Square 1. ll of the following must have congruent diagonals except a. rectangle b. square c. parallelogram d. Isosceles trapezoid 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? 2. 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 4.In parallelogram CD angle can be represented by 3x + 20 and angle can be represented by 7x 40. Find the measure of each angle of the parallelogram. 5. In rhombus CD below, what is the measure of angle D? 6.Which statement is false? 1) ll parallelograms are quadrilaterals. 2) ll rectangles are parallelograms. 3) ll squares are rhombuses. 4) ll rectangles are squares. 7.The following represents a cyclic quadrilaterals. Find the values of all variables shown. 8