Unit 6 Review Geometry Name Date: Section: CONSTRUCTION OF A SQUARE INSCRIBED IN A CIRCLE. Key Idea: Diagonals of a square are of each other.

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1 Name ate: Section: ONSTRUTION OF SQURE INSRIE IN IRLE Key Idea: iagonals of a square are of each other. Steps: 1) raw a. 2) the diameter. 3) onnect the four points on the circle to make the of the square. REVIEW PKET For each question make sure to write all formulas, substitutions, and show all work. learly label your work and clearly identify your answers. IG 1. If is translated such that I maps to H, which type of quadrilateral will be formed? a. Explain your reasoning: b. What will be the slope of HG '? 2. Name the type of quadrilateral that will be formed by reflecting the following triangles into the line: a. b.

2 3. TVWX is a rhombus. Find the following: TV m VTZ m XWV m ZVW 4. Write the equation of the line that contains the diagonal RY of rhombus GRY with G(0,9) and (4,-3): G 5. Given, determine the value of y. (12y + 10) (15x + 5) (16x 2) 6. Given is a rectangle with m = 67 and m FE = 34, find m FE. F E G

3 7. Rhombus PNWL, NW = 12, and m WLP = 144. Find PN, m LWP and m PNW. raw and label a diagram to help justify your answer. 8. quadrilateral has vertices with coordinates (-3,1), S(0,3), P(5,2), and (-1,-2). lassify the quadrilateral using coordinate geometry and explain your reasoning. What would you calculate to prove SP is not an isosceles trapezoid? Give two options: In rectangle with the diagonals intersecting at E, find the length of E when = 8x-3 and = 4x+17. e sure to draw a diagram first!

4 10. The diagonals of a rhombus measure 8 inches and 16 inches, respectively. What is the perimeter of the rhombus? Write your answer in simplest radical form. (raw and label a diagram to justify your answer.) 11. In parallelogram, the diagonals and intersect at E. raw a picture and determine which statement must be true: 12. In the diagram of trapezoid,,. If m = (4x + 20) and m = (3x 15), find m. 13. Find the value(s) of x so that is an isosceles trapezoid with bases and. (7x + 16) (x 2 + x)

5 14. XY is the midsegment of the trapezoid. Find the value of x. X R O (x 2 + 6) (6x) (x ) P Y S 15. Quadrilateral has diagonals and. What information is not sufficient to prove is a parallelogram?. and bisect each other. and. and. and 16. In quadrilateral, the diagonals bisect its angles. If the diagonals are not congruent, quadrilateral must be a. Square. Rectangle. Rhombus. Trapezoid 18. When a quadrilateral is reflected over the line y=x, which geometric relationship is not preserved?. ongruence. Orientation. Parallelism. Perpendicularity 19. If the diagonals of a quadrilateral are congruent but do not bisect each other, the quadrilateral may be a(n):. Rectangle. Isosceles Trapezoid. Rhombus. Square 20. In quadrilateral, each diagonal bisects opposite angles. If the m 70, then must be a. Rectangle. Trapezoid. Rhombus. Square

6 21. In rhombus, diagonals and intersect at E. What kind of angle is. cute. Straight. Right. Obtuse E? 22. Three vertices of parallelogram FGH are (-9,4), F(-1,5) and G(2,0).. Write the equation of the line that contains the side of the parallelogram through vertex H.. State the coordinates of vertex H. 23. State the coordinates of vertices H and P of square HPY given (0,5) and Y(-10,-1).

7 24. Prove quadrilateral with vertices (-3,2), (-1,4), (8,-5), and (6,-7) is a rectangle. Make sure to show all of your work including formulas, substitutions, etc. learly label your work. 25. Given quadrilateral and its image EFGH. escribe a sequence of rigid motions that maps onto EFGH. e specific. F G E. List the properties that are preserved under all rigid motions: H. Fill in the blanks:. If, then EF. If, then EF.

8 26. Given: bisects.. Prove: is a parallelogram Hint: first prove E E and use PT E Given: is a parallelogram bisects FG F Prove: FE GE Hint: first prove EF EG then use PT E G

9 Review Packet Unit 6 nswer Key 1. Parallelogram a. Translations preserve distance and slope so IG HG '& IG HG '. quad w/1 pair of opp sides parallel & congruent is a parallelogram. (ould also use parallel and congruent translation vectors) b. the same slope as IG TV m VTZ 20 m XWV = 40 m ZVW = y 3 ( x 2) 3 9. E=18.5 (x=5) 10. Perimeter = 6. m FE = y=5 7. PN=12 m LWP inches m PNW m = 60 (x = 25) x = 8 or x = -2 (oth check) a. Rhombus (4 congruent sides and perpendicular diagonals). b. Square (4 congruent sides parallelogram and rhombus, 1 right angle rectangle) 8. SP is a trapezoid since one set of opposite sides are parallel (S P ); 1. P S (congruent diagonals) or 2. SP (congruent legs) 14. x= ) 1 to F : y 0 ( x 2) 8 5 to FG : y 4 (x 9) 3 ) H(-6,-1) 23. H and P are located at (-8,7) and (-2,-3) (note, they are interchangeable) 24. nswers will vary depending on method chosen to prove parallelogram and then rectangle. Examples: 1 st prove parallelogram: o Since the slopes of & = -1 and the slopes of & =1, then and. Since both sets of opposite sides are, then quadrilateral is a parallelogram. o Since = 2 2 = and = 9 2 =, then and. Since both sets of opposite sides are congruent, then quadrilateral is a parallelogram. o Since the midpoints of & are both (2.5, -1.5), then the diagonals bisect each other so quad is a. 2 nd prove rectangle: o Since the slopes of =1 & =-1 are opposite reciprocals, then. Since is a right, then parallelogram is a rectangle. o Since = 170 =, then. Since the diagonals are congruent, then parallelogram is a rectangle Examples: Line reflection over the y-axis followed by a translation <0,-4> (down 4); Translation of <-4,-4> followed by a reflection over the line x = -2. ngle Measure, istance, Parallelism, Perpendicularity. E" FG HG

10 15. Prove is a parallelogram bisects E E E E is a parallelogram 1. Given 2. alt int ' s lines 3. Given 4. Segment bisector 2 congruent segments 5. Vertical angles are congruent 6. S S ' s (1,5,7) 7. PT 8. Quadrilateral w/1 set of opposite sides & 1 3 Note: could also use PT to get diagonals bisect each other using E E. (steps 7&2) Prove FE GE 1. is a parallelogram ; FG bisects EF EG 7. FE GE E E 1. Given 2. opposite sides 3. lines alt int 's 4. Given 5. Segment bisector 2 congruent segments 6. S S (4, 4, 6) 7. PT 3 2 Note: could instead use vertical angles and S. 1 4