Geometry Honors. Midterm Review

Transcription

1 eometry Honors Midterm Review

2 lass: ate: I: eometry Honors Midterm Review Multiple hoice Identify the choice that best completes the statement or answers the question. 1 What is the contrapositive of the statement below? If you live in Tallahassee, then you live in Florida. If you do not live in Florida, then you do not live in Tallahassee. If you do not live in Florida, then you live in Tallahassee. If you do not live in Tallahassee, then you do not live in Florida. If you live in Florida, then you live in Tallahassee. 2 has endpoints (5, 3) and ( 8, 9). To the nearest tenth, what is the distance, in units, from point to the midpoint of the segment? F H 7.7 J In this drawing, line p is parallel to line j and line t is perpendicular to. What is the measure of?

3 I: 4 lejandra is playing pool. The path of the ball is shown in the diagram below. What is the measure of 1? F H 104 J Three angles of quadrilateral have measures 67, 96, and 113. What is the value of x?

4 I: 6 In the quadrilateral below, what is the measure of one of the interior angles? F H 72 J 75 7 How are the angle of a triangle and the exterior angle of the triangle at the vertex related? They are complementary angles. They are supplementary angles. They are congruent angles. They are vertical angles. 8 lassify triangle XYZ according to its angle measures and side lengths. F H J acute, equilateral acute, isosceles obtuse, scalene obtuse, isosceles 3

5 I: 9 Point is the centroid of triangle PQR below. If RL = 15, what is L? Parallelogram LMNO has vertices L(8, 6), M( 3, 9), N( 6, 2), and O(5, 5). Which of the following classification(s) apply to LMNO? Identify all that apply. F H J square and rectangle rectangle square and rhombus square, rectangle, and rhombus 4

6 I: 11 Quadrilateral HIJK has the vertices shown below. Which of the following would NOT be sufficient to show that HIJK is a parallelogram? HK and IJ have the same slope, and HI and JK have the same slope. HK = IJ and HI = JK. HJ = IK HK and IJ have the same slope, and HK = IJ. 5

7 I: 12 In the proof below, which triangle congruence property is used to show that opposite sides of a parallelogram are congruent? Statement Reason 1. Ä and Ä 1. efinition of a parallelogram. 2. lternate interior angles formed by 2. and parallel lines and a transversal are congruent Reflexive Property of ongruence 4. 4.? 5. and 5. PT F H J S S SS SSS 6

8 I: 13 In the proof below, which property about parallelograms is being proved? Statement Reason 1. Ä and Ä 1. efinition of a parallelogram 2. m + m = 180 m + m = Same-side interior angles are supplementary. 3. m + m = 180 m + m = Same-side interior angles are supplementary. 4. m + m = m + m 4. Substitution property of equality 5. m = m 5. Subtraction property of equality 6. m + m = m + m 6. Substitution property of equality 7. m = m 7. Subtraction property of equality 8., 8. efinition of congruent angles onsecutive angles are supplementary. iagonals of a parallelogram bisect each other. Opposite angles are congruent. Opposite sides are congruent. 7

9 I: 14 In the proof below, which statement about kite EFH is being proved? Statement 1. EF EH and F H 1. efinition of kite Reason 2. E E 2. Reflexive Property of congruence 3. EF EH 3. SSS 4.? 4. PT F H J E E F F F H 15 Quadrilateral RSTU has exactly one pair of congruent opposite angles. Which type of quadrilateral could RSTU be? kite rectangle trapezoid parallelogram 16 In quadrilateral LMNO, LN and MO are congruent. Which type of quadrilateral could LMNO NOT be? F H J rectangle kite square rhombus 8

10 I: 17 If a quadrilateral has exactly two pairs of consecutive angles that are supplementary, which type of quadrilateral is it? rhombus parallelogram trapezoid kite 18 Which of the following is not necessarily a property of a parallelogram? F H J oth pairs of opposite sides are parallel. oth pairs of opposite sides are congruent. iagonals are congruent. iagonals bisect each other. 19 Which of the following is not necessarily a property of a rhombus? ll sides are congruent. ll angles are congruent. iagonals are perpendicular. iagonals bisect each other. 20 Which of the following statements is true? F H J ll parallelograms are rhombi. ll rhombi are squares. ll rectangles are squares. ll squares are rectangles. 9

11 I: 21 The Florida state flag in Mr. Wesson s homeroom has four right angles and the dimensions shown below. Which of the following is the best classification for the shape of the flag? parallelogram rhombus square rectangle 22 Which of the following is NOT a method for proving triangle congruence? F H J SSS ongruence SS ongruence S ongruence SS ongruence 23 iven: LM KJ. Which additional piece of information would be sufficient to prove that triangles HLM and IKJ are congruent? HIKL is a parallelogram. HIKL is a rectangle. HM IJ HLM IJK 10

12 I: 24 iven: STUV is an isosceles trapezoid. Prove: SU TV What is the missing reason in step 2? Statement Reason 1. SV TU 1. Legs of an isosceles trapezoid are congruent. 2. SVU TUV 2.? 3. VU UV 3. Reflexive Property of ongruence 4. SVU TUV 4. SS 5. SU TV 5. PT F H J PT ase angles of a trapezoid are supplementary. Symmetric Property of ongruence ase angles of an isosceles triangle are congruent. 11

13 I: 25 iven: is a kite. Prove: E E Which triangle congruence statement is missing in step 4? Statement 1. is a kite. 1. iven Reason 2. ; 2. efinition of a kite Reflexive Property of ongruence 4.? 4. SSS 5. E E 5. PT 6. E E 6. Reflexive Property of ongruence 7. E E 7. SS E E E E E 26 Which group of segment lengths can be used to form a triangle? F 6, 8, 14 5, 9, 12 H 3, 6, 15 J 2, 4, 7 12

14 I: 27 In triangle below, which angle has the greatest measure? ll three angles have the same measure. 28 In each of the triangles below, two of the sides are congruent to corresponding sides in the other triangles. The included angles are all different. Which triangle has the greatest perimeter? F H J triangle triangle EF triangle HJ triangle LMN 29 Two sides of a triangle are 5 inches and 9 inches. Which can be the length of the third side? 3.8 inches 5.2 inches 14.1 inches 16.5 inches 13

15 I: 30 Which statement is true about in triangle below? F m = 85 m < 85 H m > 85 J m = Triangle shows the lengths of the three sides. Which expression gives the greatest value? m + m m + m m + m 3 4 m 32 In triangles and EF below, E and EF, but is smaller than E. Which could be the length of F? F H J 15 inches 16 inches 17 inches 18 inches 14

16 I: 33 In the figure below, NP is the altitude drawn to the hypotenuse of MNO. If NP = 9 and MP = 15, what is the length of OP? Tracy cut out a piece of construction paper in the shape of a rhombus. Which of the following statements is a conjecture she NNOT make about the paper? F H J The sides of the paper have the same length. The diagonals of the paper bisect each other. The diagonals of the paper have the same length. The diagonals of the paper are perpendicular. 35 Name three points that are collinear. M, L, R Q, L, M L, P, T R, S, K 15

17 I: 36 Find the value b and length H, given H is between and I. I = 5b + 1, HI = 4b 5, HI = 7 F b = 1.2, H = 6.8 H b = 3, H = 9 b = 1.22, H = 7.11 J b = 3, H = 16 etermine whether WX and YZ 37 WÊ Ë Á 2, 1 ˆ, X Ê Ë Á4, 1 ˆ, Y Ê Ë Á1, 4 ˆ, Z Ê ËÁ 5, 4 ˆ perpendicular parallel neither are parallel, perpendicular, or neither. Write an equation in point-slope form of the line having the given slope that contains the given point. 38 m = 2 3, Ê 15 4, 1 ˆ ËÁ 2 F y = 2 Ê 3 x 15 ˆ ËÁ 4 y 15 4 = 2 Ê 3 x + 1 ˆ ËÁ 2 H y = 2 Ê 3 x + 15 ˆ ËÁ 4 J y = 2 3 x

18 I: iven the following information, determine which lines, if any, are parallel. State the postulate or theorem that justifies your answer. 39 LHO NKP c Ä d; congruent corresponding angles a Ä b; congruent corresponding angles a Ä b; congruent alternate exterior angles c Ä d; congruent alternate exterior angles Find each measure. 40 m 1, m 2, m 3 F m 1 = 64, m 2 = 74, m 3 = 52 H m 1 = 47, m 2 = 74, m 3 = 69 m 1 = 64, m 2 = 47, m 3 = 52 J m 1 = 47, m 2 = 59, m 3 = 64 17

19 I: Use the figure below to answer quesetion 43. ΔRM, ΔMX, and ΔXFM are all isosceles triangles. 41 If m FX = 96, what is m FMR? Z is an altitude, YW = 9x + 38, and WZ = 17x. Find m WZ. F 34 H J XW is an angle bisector, YXZ = 7x + 39, WXY = 10x 13, and XZY = 10x. Find m WZX. Is XW an altitude? 50; no 50; yes 32; yes 32; no 18

20 I: etermine the relationship between the lengths of the given sides. 44 ZX, YX F ZX < YX H ZX > YX ZX = YX raph each figure and its image under the given translation. 45 with endpoints ( 3, 2) and ( 4, 3) under the translation left two units and down one unit 19

21 I: 46 ΔXYZ with endpoints X( 2, 2), Y( 4, 4), Z( 3, 4) under the translation (x, y) (x + 2, y 2) F H J 47 How do you write the inverse of the conditional statement below? If m 1 = 60, then 1 is acute. If m 1 = 60, then 1 is not acute. If 1 is not acute, then m If 1 is acute, then m 1 = 60. If m 1 60, then 1 is not acute. 20

22 I: Short nswer Write a two-column proof of the theorem. 48 If m + m H = 180, then FH Ä. 49 Find x, PQ, QR, and RP if PQR is an isosceles triangle with PQ QR. Write a two-column proof. 50 iven: Square HJK Prove: ΔHK ΔJKH 21

23 I: 51 salesperson travels from city to city and then to city. From city, the salesperson travels directly back to city as shown in the diagram below. Write the lengths of the legs of the trip in order from least to greatest. 52 In a botanical garden, a regular octagonal greenhouse was designed especially for orchids. Find the sum of the measures of the interior angles and an exterior angle of the greenhouse. 22

24 I: eometry Honors Midterm Review nswer Section MULTIPLE HOIE 1 NS: ST: M NS: ST: M NS: ST: M NS: F ST: M NS: ST: M NS: ST: M NS: ST: M NS: J ST: M NS: ST: M NS: J ST: M NS: ST: M NS: ST: M M M NS: ST: M M M NS: J ST: M M M NS: ST: M NS: ST: M NS: ST: M NS: H ST: M NS: ST: M NS: J ST: M NS: ST: M NS: J ST: M NS: ST: M M NS: J ST: M M M NS: ST: M M M NS: ST: M NS: ST: M NS: F ST: M NS: ST: M NS: ST: M NS: ST: M NS: J ST: M NS: ST: M NS: H ST: M NS: ST: L M NS: H ST: M M NS: ST: M

25 I: 38 NS: F ST: M NS: ST: M NS: H ST: M M M M NS: ST: L M NS: F ST: L M NS: ST: L M NS: H ST: L M NS: ST: M M NS: ST: M M NS: ST: M SHORT NSWER 48 NS: Sample: iven: m + m H = 180 Prove: FH Ä Proof: Statements Reasons 1. m + m H = iven 2. and are a linear pair. 2. efinition of linear pair 3. m + m = The sum of the measures of a linear pair is m + m H = m + m 4. Substitution Property 5. m H = m 5. Subtraction Property 6. H 6. efinition of congruent angles 7. FH Ä 7. If corresponding angles are congruent, then lines are parallel. ST: M NS: x = 9, PQ = 19, QR = 19, RP = 10 Use 2x + 1 = 3x 8 to find the value of x. Replace x to find the lengths of PQ, QR, and RP. ST: M M

26 I: 50 NS: Sample: iven: Square HJK Prove: ΔHK ΔJKH Proof: Statements Reasons 1. HJK is a square. 1. iven 2. K JH 2. efinition of a square 3. H JK 3. efinition of a square 4. HK KH 4. Reflexive Property 5. ΔHK ΔJKH 5. SSS Postulate ST: M M NS: city to city, city to city, city to city If one angle of a triangle has a greater measure than another angle, then the side opposite the greater angle is longer than the side opposite the lesser angle. ST: L M NS: 1080, 45 To find the sum of the measures of the interior angles of a regular polygon, use the formula 180 ( n 2). To find the measure of each exterior angle of a regular polygon, use the formula 360 n. ST: M M