Unit 5 Test Date Block

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1 Geometry B Name Unit 5 Test Date Block 60 ANSWERS Directions: This test is written to cover Unit 5. Please answer each question to the best of your ability. If multiple steps are required, it is expected that you will show those steps. If the appropriate work is not shown, then points may be deducted. 1. Which of the figures below does NOT represent a polygon? Explain why. ( points) A. B. C. A because the segments do not meet at endpoints, there is overlap For questions & 3, use the figures A, B, and C below. A. B. C.. Explain why figure A a regular convex polygon. ( points) All sides and angles congruent; all diagonals drawn inside 3. Explain why figure B is an irregular concave polygon. ( points) Not all angles congruent; diagonals can be drawn on outside 4. Determine if the figures have line symmetry. If so, draw ALL lines of symmetry. (1 point each) a. Oval b. Parallelogram No line symmetry 5. Determine if the figures have rotational symmetry. If so, give the angle of rotational symmetry and the order of rotational symmetry. (1 point each) a. Square b. Right Triangle 90 ; 4 No rotational symmetry

2 6. What is the sum of the measures the interior angles of a convex nonagon? Show work to support your answer. ( points) (9 ) What is measure of each exterior angle of a regular 4-gon? Show work to support your answer. ( points) What is the measure of each interior angle of a regular octagon? Show work to support your answer. ( points) (8 ) Find the value of a in hexagon ABCDEF. Show work to support your answer. ( points) a 5a 4a 5a 3a 5a 70 4a 70 a 30 a = Find the value of a in the quadrilateral below. ( points) a a a 60 a = Given parallelogram ABCD to the right, find the following and explain your reasoning. (1 point each) mabc 114 ; CD = 34, BD = 56 a. AB = 34; opposite sides are congruent B C b. BE = 8; diagonals bisect each other A E D c. m BCD = 66 ; consecutive angles are supplementary d. m ADC = 114 ; opposite angles are congruent

3 1. In rectangle ABCD, find the following and explain your reasoning. mbda (1 point each) CD 0, CE, and 7 a. AB = 0; opposite sides are congruent b. AE = ; diagonals bisect each other c. BD = 44;diagonals are congruent d. mabd = 63 ; all angles are right angles, In rhombus QRST, find the following and explain your reasoning. (1 point each) mrps 5a 15, mpqr a 3 R a. QT = 7; all sides congruent 4x+15 8x+3 x+9 b. a = 15; diagonals perpendicular Q P S c. TR = 30; diagonals bisect each other d. m QTP = 57 ;cons s supp & diagonals bisect opposite angles T 14. Fill in the blanks for each diagram. You may have to use some trigonometry. (1 point each blank) a. Rhombus ABCD b. Square FGHI m AEB = 90 m FGH = 90 m DAC = 65 m FGI = 45 m ABE = 5 m IHF = 45 AB = 4.0 FH = 14.0 (Round to the nearest tenth.) (Round to the nearest tenth.) Show work below. Show work below. 1.7 cos FH AB FH AB cos FH

4 Determine if each of the following is enough information to conclude that the quadrilateral is a parallelogram, rectangle, rhombus, or square. Be sure to state the reason. All questions are quadrilateral QUAD with diagonals intersecting at point X. ( points each) 15. QUA ADQ, UQD UAD PARALLELOGRAM both pairs of opposite angles are congruent 16. QU UA AD QD, QUA 90 SQUARE it s a rhombus (all four sides congruent), which also makes it a parallelogram; it s also a rectangle (a parallelogram with one right angle) 17. QX 10, UX 10, AX 10, DX 10 RECTANGLE it s a parallelogram (because diagonals bisect each other) with diagonals congruent 18. For each statement, write A if the statement is always true, S if the statement is sometimes true, and N if the statement is never true. (½ point each) a. A parallelogram is a quadrilateral. A b. A quadrilateral is a square. S c. A rectangle is a square. S d. A square is a rectangle. A e. A parallelogram is a rhombus. S f. A rhombus is a parallelogram. A For questions 19, circle one response. (1 point each) 19. Which of the following quadrilaterals have diagonals congruent? b. rectangle, square, rhombus c. rhombus, square, d. rectangle, square 0. Which of the following quadrilaterals have perpendicular diagonals? b. rhombus, square, rectangle c. rectangle, square d. rhombus, square

5 1. Which of the following quadrilaterals have diagonals bisect each other? b. parallelogram, rhombus c. parallelogram, rectangle d. parallelogram, rhombus, square. Which of the following quadrilaterals have diagonals bisect the opposite angles? b. rectangle, rhombus, square c. rhombus, square d. rectangle, square 3. Determine if quadrilateral ABCD with the following coordinates is a parallelogram, rectangle, or rhombus, or square. You must prove your answer and explain your reasoning. ( points each) A( 4, ), B( 1,4), C(1,1), D(, 1) a. Is it a parallelogram? AC :, 1.5, BD :, 1.5,1.5 Yes, the diagonals bisect each other since they have the same midpoint y b. Is it a rectangle? 4 AB : 1 ( 4) BC : 1 ( 1) Yes, it s a parallelogram with one right angles (since the slopes are opposite reciprocals) x c. Is it a rhombus? 1 1 AC : 1 ( 4) BD : ( 1) 1 1 Yes, it s a parallelogram with diagonals perpendicular (since the slopes are opposite reciprocals) d. Is it a square? Yes, because it s a rectangle and a rhombus

6 BONUS: 1. Three vertices of parallelogram ABCD are A( 4, 3), B(1,5), and C(8,6). Find the coordinates of vertex D. ( points) y x An interior angle of a regular convex polygon is 144 degrees. How many sides does the polygon have? ( points) 3. Ima Smartalek claims that any quadrilateral with perpendicular diagonals has to be a rhombus. Draw a figure (neatly!) that proves him wrong. Use the graph if you want, or blank space on your paper. ( points) 8 y x 4 6 8

Any questions about the material so far? About the exercises?

Any questions about the material so far? About the exercises? Here is a question for you. In the diagram on the board, DE is parallel to AC, DB = 4, AB = 9 and BE = 8. What is the length EC? Polygons Definitions: