Geometry Questions

6 Determine if the following statement is valid or invalid An object is green if and only if it is not blue Valid O Invalid

Identify the hypothesis and the conclusion of the conditional stateme If it is hot then I will go to the beach Hypothesis I will not go to the beach Conclusion it is hot O Hypothesis I will go to the beach Conclusion it is hot O Hypothesis it is hot Conclusion I will go to the beach O Hypothesis Conclusion it is not hot I will go to the beach

First we wish to find polar coordinates with r 0 To find the positive value of r we choose the positive square root to solve for r SE 50 5 2 We are also asked to find such that 0 8 2 As 5 5 is in the fourth quadrant we choose a value of 0 in the fourth quadrant with 0 0 2 such that tan 0 1 7 4 7 8 To finish we find that polar coordinates of the given point with the required conditions are as follows 77 7T 5 2 4 4 r 8 50 r 5 Step 3 We are asked to find a second pair of polar coordinates for the Cartesian coordinates 5 5 We have found the following 2 50 We must now find polar coordinates with r 0 To find the negative value of r we choose the negative square root to solve for r

22 Given Prove DG DE DH DF LDGH LE Statements 1 2 LD LD 3 ADGH ADEF 4 PROOF 1 2 3 4 2 E D Reasons H F

14 Given Prove D A E ADET and ABCD AABE ACTB B Statements 1 ADET and ABCD 2 AB DT 3 LEBA LT 4 ED CB 5 LE LCBT 6 AABE ACTB PROOF Reasons 1 2 Opposite sides of a are 3 4 5 6

Classify as true or false a Any two rectangles are similar b If an angle of one rhombus is congruent to an angle of a second rhombus then the two rhombi are similar

In Exercises 5 to 8 name the method AA SSS or SAS that is used to show that the triangles are similar 5 WU 2 TR WV 2 TS and UV RS R T SU W V

In Exercises 9 to 12 name the method that explains why ADGH ADEF DG 9 DE E G DH DF D H LL F

1 Classify as true or false a If the midpoints of two sides of a triangle are joined th triangle formed is similar to the original triangle b Any two isosceles triangles are similar

Find the enlargement ratio of the circle C with center 2 8 of radius 2 units and circle C with center 4 4 of radius 6 units when C is transformed to C 1 3 5 Reset button enabled after this assessment Questions0 10 1 Reset 3 2 4

Find the measure of angle A A 8 Xx 5 B O 30 degrees O 45 degrees O 60 degrees 7 C

Find the measure of the side AB Round your answer to the nearest whole number A 12 45 C 20 22 23 a 30 B

The smallest side of a triangle is 5 cm and the largest side is twice the smallest side and the included angle between these sides is 65 Find the measure of the third side of the triangle 2 5 cm 7 5 cm 9 cm 12 cm

The length of the side AC is 8 cm Find the measure of the side AB in the given figure co 99 4 3 cm 7 9 cm 13 4 cm 14 9 cm 32 B

Find the measure of the missing side in the triangle ABC Round your answer to the nearest whole number A 15 O17 20 18 9 66 13 B

The two sides of the triangle ABC are 3 cm 5 cm and third side is 4 cm greater than the smallest side Find the measure of the smallest angle in the triangle ABC Round off to the nearest degree 180 120 38 22

An aircraft tracking station determines the distance from a common point to each aircraft and the angle between the aircrafts If the angle between the two aircraft is equal to 49 and the distances from the point to the two aircraft are 50 km and 72 km find the distance between the two aircraft Aircraft 1 72 km O 50 km O 52 km 54 4 km X 49 Aircraft 2 50 km Res com Que 1 4 7 10

factor of the dilation for transforming the circle C to C 10 C 8765432 7 2 C 10 9 8 7 6 4 3 2 1 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 27 O Translation 7 units to the left and 6 units down Scale factor enlargement ratio Translation 7 units to the right and 6 units up Scale factor enlargement ratio Translation 7 units to the right and 6 units down Scale factor enlargement ratio 2 com Ques 1 4 7 F 10

If the image is smaller than the original figure then the dilation is a ar congruent O enlargement reduction rigid transformation

Circle C center 0 2 and radius 6 Circle C center 0 6 and radius 2 Which of the following transformation translation dilation is performed from C to C Translation 8 units up Scale factor enlargement ratio 3 Translation 8 units right Scale factor reduction ratio 1 3 Translation 8 units left Scale factor enlargement ratio 3 O Translation 8 units down Scale factor reduction ratio 1 3

Circle A center 4 0 and radius 6 Circle B center 11 0 and radius 4 Which of the following transformation is performed from circle A to circle B O Translation 15 units right and scale factor O Translation 15 units left and scale factor O Translation 15 units right and scale factor

A scalene triangle has sides that measure 4m 11m and 8m Find the measure of the smallest angle of this triangle 16 2 34 0 129 8 135 6

Two ships 1600 ft apart detect a submarine directly between them The angle of depression from the first ship to the submarine is 40 and from the second ship is 28 Find the distance between the first ship and the submarine 1109 ft 900 ft 1600 ft 28

Question 7 Points 2 The measure of an included angle between two sides is 45 and the measures of the sides are 5 m and 8 m Find the measure of the third side O 4 5 m O 5 5 m 5 7 m 5 9 m RE CO

Circle A center 7 0 and radius 5 Circle B center 10 0 and radius 2 Which of the following transformation is performed from circle B to circle A to prove that the two circles are similar Translation 3 units left and scale factor Translation 3 units right and scale factor O Translation 3 units left and scale factor Reset bu enabled a this assessm Reset Questions 1 3

D Given Find AABC APRC MZA 67 PC 5 CR 12 PR 13 AB 26 a m B b m RPC c AC d CB P A R B

23 Given Find 24 Given Find DE 4 AC 20 EC BC BC AD 4 AC DB AE AE 18 C S E Exercises 21 24

1 a Does the similarity relationship have a reflexive property for triangles and polygons in general b Is there a symmetric property for the similarity of triangles and polygons c Is there a transitive property for the similarity of triangles and polygons

8 Given that rectangle ABCE is similar to rectangle MNPR and that ACDE APQR what can you conclude regarding pentagon ABCDE and pentagon MNPQR E I D C R Q P

9 Given Find M R Q AMNP AQRS m M 56 m R 9 QR 6 RS 7 MP 12 MN a m N b m P S P c NP d QS

c Al A1 13 In the drawing AHJK If HK find FG AFGK 6 KF 8 and HJ 4 14 In the drawing AHJK AFGK 6 KF 8 and FG 5 If HK find HJ F K G Exercises 13 14

3 a Are any two regular pentagons similar b Are any two equiangular pentagons similar

A B a Exercises 15 20 17 Quadrilateral ABCD BC n HJ H 16 Quadrilateral ABCD quadrilateral HJKL If mA X m J x 50 m D x 35 and mZK 2x 45 find x J b quadrilateral HJKL If AB 5 10 and JK n 3 find n 18 Quadrilateral ABCD mZD 90 AD length of diagonal HK not shown K quadrilateral HJKL If 8 DC 6 and HL 12 find the 19 Quadrilateral ABCD quadrilateral HJKL If MZA 2x4 m H 68 and m D 3x 6 find m T

B Exercises 5 6 6 a If AABC A b If AABC C to LN of AXTN T AXTN which angle of AABC corresponds N side AC of AABC AXTN which side of AXTN corresponds to

11 If sin a 6 TT 11 2 11 2 following expressions Be sure to simplify radicals and rationalize the denominator a cos a a 0 and cos 1 0 B find the exact value of each of the b sin 3 c Enter the numerator and denominator separately in the boxes below If the denominator is 1 enter the number 1 Do not leave either box blank The sign in the denominator should be positive Answer sin a B

1 point FORMULA FROM CUBIC GRAPH The figure shows the graph of a cubic polynomial G The function graphed is f x Hint You may write the function as f x a r b x c z d where b c and d are integers and a is a

On the Chapter 5 Test Supplement handout write an indirect proof to show that AB AD 3 points 2 3 4

The figure shows the graph of r as a function of 8 in Cartesian coordinates Use it to sketch the corresponding polar curve 1 5 2 0 1 5 1 0 0 5 1 0 0 5 R y 1 5 1 0 0 5 0 5 1 0 1 5 0 5 21 1 0 3 2 1 3 2 0 2 2 X 1 5 1 0 0 5 1 5 1 0 0 5 0 5 1 0 1 5 0 5 26 X 15 1 0 76 F

The hydraulic retention time for a single reactor or treatment unit can be calculated by dividing the volume of the reactor by the influent flow rate A gravity sand filter bed that is rectangular with horizontal dimensions 6x18 ft has an influent flow rate of 50 gpm and a hydraulic retention time of 216 minutes How deep is the sand bed Round your answer to the nearest hundredth hint first calculate the volume of the filter bed then use the known dimensions to calculate the missing one Y

Find all x in R that are mapped into the zero vector by the transformation x Ax for the given matrix A 1 5 6 3 A 0 1 3 2 8 6 2 OA There is only one vector which is x OB X OC X 2 5 NN 132 T 2 6 N 0 accen

Find a non trivial solution to the following homogeneous system of equations 4 3i x 4y 0 118i r 8 12i y 0 Enter your answers in the form a bi

Find the point on the surface z 16 x y at which the tangent plane is parallel to the plane x y z 4

3 Identify the period label your vertical scale and ALL important information then graph sec x 7

Given that AABC has mZC 88 a 12 and b 22 find the remaining side length c and angles A and B rounded to the nearest tenth Provide your answer below A 22 C 88 12 C B

nd integers that are upper and lower bounds for the real zeros of the polynomial Be sure the lower bound is the largest possil P x x2x x 9x 2 smaller value larger value

11 Given that cos M in Quadrant II and sin N 17 Give exact answers for all questions Give exact answers sin M Give exact answers cos N Give exact answers tan 2N Give exact answers cos MN sin Give exact answers M 1 2 Give exact answers sin M cos N tan 2N cos M N sin M 1 1 2 sin M N 4 in Quadrant III answer the following 5

Convert the following angle to degrees minutes and seconds form 29 369 The answer is 0 Simplify your answers Round to the nearest second as needed

A tree casts a shadow 24 ft long At the same time the shadow cast by a vertical 7 ft post is 12 ft long Find the height of the tree The tree s height is ft www

Find the unknown angle measure in the pair of similar triangles angle B angle M O 0 0 www angle A Simplify your answers Type an integer or a fraction 27 A N17 B 109 K 170 C

Find the measure of each marked angle 0 x x 50 0 0 180 3x Simplify your answers Type integers or fractions C 40 x 50 180 3x 0