.~I~.~_~_~-~-~.~-~-~-~.~-~-~-~-~-~-~-~-~- Complete the table. Place a check mark under the name of each figure for which the property is a/ways true.

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1 Date Pd -- ~~.~.~.~I~.~'~'~.~.~.~,~,~.~.~#~.~.~.~.~,~,~.! GEOMETRY _ - RHOMBUS, RECT. & SQ. REVIEW! Name --.~I~.~_~_~-~-~.~-~-~-~.~-~-~-~-~-~-~-~-~- Complete the table. Place a check mark under the name of each figure for which the property is a/ways true. 1 The diagonals are perpendicular. 2 The figure has four right angles. 3 The opposite sides are congruent. 4 The diagonals are congruent. 5 The figure has four congruent sides. 6 The diagonals bisect each other. 7 The consecutive <s.are supplementary. 8 Each diagonal bisects a pair of opp. <so Parallelogram Rhombus Rectangle Square Use the diagram for problems MNPQ is a rhombus. Find the meas. of each angle. Use the diagram for problems GHJK is a rhombus, with GJ = 42. Find the length of each segment. G If Q 9 m<1= 12 m<nmq= 10 m<mnp= 13 m<2= 11 m<3= 14 m<4= K 15 GH= 18 HJ= 16 LJ= 19 LH= 17 KH= Use the diagram for problems ABCD is a rhombus. Find each of the following. A B 20 BC= 24 m<adc= 21 AB = 25 m<3 = 22 m<1= 26 AE= 23 m<2 = 27 AC=

2 Use the diagram for problems ABCD is a rectangle, with AC = 18. Find each of the following. 28 m<bcd= -31 m<1 = 29 m<3 = 30 m<6 = 32 m<4= _ 33 AE= _ 34 m<2 = 35 m<5 = 36 DB= Use the diagram for problems GHJK is a rectangle, that is not a square. Answer true or false. T>i<T K J 37 GHJK and its diagonals form four congruent triangles. 38 GHJK and its diagonals form four isosceles triangles. 39 < 1;;< 2 40 AGHJ;; I!JKG 41.GJ is a line of symmetry. 42 AGMK:: AHMG

3 & Polygons and Quadrilaterals Choose the best answer. 1. Which must be a regular convex AO polygon? C<{ BODU 5. PSTV is a parallelogram, and V is the midpoint of PR. Q P/0s"R v Which is NOT necessarily true? -- ATR=TV C QPIITV B OS = SP. 0 ST is a midsegment. FO 2. Which is an irregular concave polygon? H<{ GOJ U 6. Which quadrilateral MUST be a parallelogram? I I' 3. The consecutive angles of a parallelogram measure (x + 30) and 4xO. What is the measure of the smallest angle? A 10 C 40 B PQRS is a parallelogram. Find x. s~~ 7. What is the sum of the measures of the interior angles of a regular 72-gon? A 6480 C 12,960 B 12,600 D 13, In quadrilateral WXYZ, LW= LY. Which information would. help to prove that WXYZ is a parallelogram? F WY=XZ G LX=LW H WX=XY J LX=LZ F 3 G 7 H 9 J The angles of a pentagon measure x", 2~, 3xo, 4xo, and 5~. What is the measure of the smallest angle? A 12 C 60 o 108 Original content Copyright by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. 105 Holt MCDougal Geometry

4 & Polygons and Quadrilaterals Choose the best answer. AO 1. Which MUST be a square? C[gJ 5. WXYZ is a rhombus. What is mlxyz? w BD DO y A C 1400 B 120 o Which FOH$ is NOT necessarily a rhombus? GOJ$ 3. PQRS is a rectangle. Find ST. P~12 Q 6. KLMN is a square and LN 1. NP. M ~P Which can be proved? F 6.KPN= 6KQN -- G PNIIKM H KQ=PN L J KP = :J_LN 2 N K..v t-., 16 S T A A 10 B 12 C 12.5 o 25 '~.,., '. I, 4. Quadrilateral RSTU is a parallelogram. What other information would allow you to prove that RSTU is a rectangle? F Opposite angles are congruent. G Opposite sides are congruent. H The diagonals J The diagonals bisect the angles. are congruent. Original content Copyright by Holt McDougaL Additions and changes to the original content are the responsibility of the instructor. 106 Holt McDougal Geometry "'I :1

5 ~ Polygons and Quadrilaterals Circle the best answer. 1. Which term does NOT describe the figure? A concavedc polygon B hexagon o regular 2. What is the sum of the measures of the interior angles of a 5-sided convex polygon? A 72 C 540 B What is the value of a? 6. WXYZ is a parallelogram. What is the value of x? A7 B Which MUST be a parallelogram? OL><7 Figure 1 Figure 2 A Figure 1 B Figure 2 8. If EF II GH I what additional information would allow you, to conclude that EFGH is a parallelogram? HOF E, I I A 60 B The diagonals of D ABCD intersect at X. Which is NOT true? A LDAB:=LBCD B mldab + mlcba = 180 C BC-=AD o AX-=XB Use the figure for Exercises 5 and 6. wu x 8x + 12 Y WXYZ is a parallelogram. Which is mlw? A 68 B 112 A EF:=GH B FG:=EH 9. Which is NOT always true? G A A square is a rhombus. B A rectanqleis a parallelogram. C A rhombus is a rectangle. o A square is a rectangle. 10. PQRS is a rectangle. PR = 26. What is the value of x? A 6.5 B 13 P~Q E 2x S R Original content Copyright by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor, 107 Holt McDougal Geometry

6 & Polygons and Quadrilaterals 11. RSTU is a rhombus. ml.sru = 112. Find ml.tru. R T 12. Write True or False. If EF II HG and -- EH II FG, then OEFGH is a rectangle. E,..., F G 13. Given: UVWX is a parallelogram and - - UV == Xu. Conclusion: UVWX is a rhombus. Determine whether the conclusion is valid. v x Original content Copyright by Holl McDougal. Additions and changes to the original content are the responsibility of the instructor. 114 Holt McDotJni'll Geornetrv

7 ~ Polygons and Quadrilaterals 1. Write True or False. The figure is a regular polygon. o 6. ABCD is a parallelogram. Find mlc. 7. Write True or False. The quadrilateral is a parallelogram. 2. Find the sum of the measures of the interior angles of the polygon....) 3. Find the measure of each exterior angle of a regular quadrilateral. 8. In the figure, JM II KL. Show that the quadrilateral is a parallelogram for X= 3. J K 5X-n3X+5 'UL 4. Write True or False. If AB II CD, then ABCD is a parallelogram. Use the figure for Exercises 5 and 6. OBC 2x + 4 A 0 5. ABCD is a parallelogram. Find the value of x. 9. Write True or False. A square is a rhombus. 10. ABCD is a rectangle. AD = 15, AC = 25, and DC = 20. Find BD. A~B D~C Original content Copyright by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. 113 Holt McDougal Geometry

8 Name Date Class - ~ Polygons and Quadrilaterals 11. RSTQ is a rhombus. Find mlpst. A,. ' T 12. Given: WXYZ is a parallelogram. WYand XZ' bisect each other and - - WY..L XZ. Conclusion: WXYZ is a rectangle. Determine whether the conclusion is valid. If not, tell why not. I. :,." ~"»r. 1.3: Tell whether the parallelogram is a rectangle, rhombus, or square.,,: I, Original content Copyright by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor Holt Mc:DClIlClRIGeometrv

Polygon Interior Angles

Polygon Interior Angles Polygons can be named by the number of sides. A regular polygon has All other polygons are irregular. A concave polygon has All other polygons are convex, with all vertices facing outwards. Name each polygon