Geometry Questions

The following list gives the number of public libraries in each of 9 cities 5 5 8 7 4 5 4 7 4 Find the modes of this data set If there is more than one mode write them separated by commas If there is no mode click on No mode 11 X No mode S

Find the length of the median in each trapezoid 12 14 in 13 15 20 mm 2 in 60 mm 10 yd 16 4 0 cm 30 yd Van 9 6 cm 14 17 32 m 64 m 35 ft 18

A heptagon is shown in the figure below xo The two missing angles are equal and labeled with x If the sum of all other interior angles is 675 what is the angle measure of x Round to the nearest hundredth For example if answer is x 49 5643 enter 49 56 Do not include x the degree sign in your answer

The table below summarizes the amount of milk consumed by a sample of 33 families last month Number of families Number of gallons per family 2 gallons 15 16 1 X 4 For these families what is the mean number of gallons of milk consumed Round your answer to the nearest 5

1 Which sequence of rigid motions will definitely work to take triangle GHJ onto triangle STU a b C d Rotate GHJ using center G until GH is lined up with ST and then reflect over a line halfway between G H J and STU Translate GHJ by the directed line segment GS Rotate G H J using S as the center by angle H ST Reflect G H J over ST Translate GHJ by the directed line segment GT Rotate G H J using T as the center by angle H TS Reflect G H J over ST Translate GHJ by the directed line segment GS Translate G H J by the directed line segment H T Translato C I bu the directed line coament HT

se the fact that matrices A and B are row equivalent 1 21 0 0 2 5 1 1 0 3 7 2 2 2 8 18 6 2 8 10 30 4 1 0 A B WN 01 00 00 2 0 1 2 000 a Find the rank and nullity of A rank nullity b Find a basis for the nullspace of A c Find a basis for the row space of A

2 Reflect triangle STU across line ST Which of these is a valid reason why the image of U will coincide with J a S The image of U and J are on the same side of ST and make the same angle with it at T b The image of U and J are the same distance along the same ray from T The image of U and I will not coincide after reflection over ST d Line ST is the perpendicular bisector of the segment connecting U and J because the perpendicular bisector is determined by 2 points that are both equidistant from the endpoints of a segment C T

Given LA LC CF AD Prove AE CE 14 Steps LA LL 2 CF AD LE LE C 0 B E Reasons Given Given Identity CPCTC F

Find the missing angle measures in each isosceles trapezoid 18 O 19 J K 20 W D Z 120 M 85 Z 100 X

The figure below shows a block of butter Which shape does the intersection of the vertical plane with the block of butter like O Circle O Rectangle O Triangle Square

16 iven BD bisects LABC LA LC Pune AB BL 3 Steps BD bisects LABC LA LC BD BD 4 LABD LCBD AB BC A B D Reasons Given Cel Given Identity C Definition of Bisector AAS

1 6 iven BD bisects LABC LA FLC Puse AB BL Steps BD bisects LABC LA LC BD BD LABD LCBD AB BC D Reasons Given Given Identity Definition of Bisector AAS

3 In quadrilateral EFGH HK KF and LKHE LKFG Show that quadrilateral EFGH is a parallelogram by providing a reason for each step LFKG a LEKH b AEKHAGKF c EH GF d EH GF e EFGH is a parallelogram H E K G F

15 Determine whether quadrilateral XYZW is a parallelogram Give reasons for your answer W X

1 Find the exact value of the expression Don t plug this into a calculator use your knowledge of inverse trig functions to find the exact value csc sin 1 185 11

1 Consider the right triangle ABC given below B C 25 b 25 A Part I Use the 25 angle and the sine ratio to find the length of side b to two dec places 2 points Part II You can find the length of side a using cos 25 tan 25 or the Pythagorea theorem Find the length of side a to two decimal places using one of these methods 2 points

Given Square ABCD Prove AC BD D A

0 Find the missing angles and sides in parallelogram ABCD 4 A B X 25 5 W 80 D Z C

Use rigid motions to prove that figure ABC is congruent to figure EFG B C F G

Given CD is a median AC BC Pwove LACD LB CD 3 4 5 Steps CD is a median AC BC CD CD AACD ABCD AC BC A C Reasons Given SSS D Given Identity CPCTC B

15 X 300 Find value of x in the 30 60 90 triangle Give your answer as a simplified radical

14d Determine the length of the missing sides for each special right triangle Leave answer in exa reduced radical form a 300 18 C 60

Use the diagrams to find the missing sides of the right triangles Round your results to two decimal places as needed Figure A 5 2 6 5 a

Find the area of the figure Sides meet at right angles 14 cm 7 cm 5 cm 4 cm 5 cm 5 cm 5 cm 7 cm

20 60 H Find value of x and y in the 30 60 90 triangle Give your answer as a simplified radica y x

In rhombus ABCD find the missing angles A D X B C

Find the missing value 6 4 6 X

8 8 Q The length of the hypotenuse is

Find the value for x C 8 E x 9 G F 3x 3 4 D

In rhombus ABCD find the missing angle A D X Z B C

Find the value for z 7 E 3z 1 G 2 F 2z 2 Note Solving this will result in two possible answers Always make sure the value of z produces posit lengths

A AC Given BC 11 mm AB 30 in in B C

Find the lengths of the diagonals of rectangle ABCD D A Xt 10 2x E ly 19 415 C B

Find the measures of angles A B C and D in the isosceles trapezoidl A B 2x 3y 5x 5 94

A 13 foot ladder is leaning on a tree The bottom of the ladder on on the ground at a distance of 6 feet from the base of the tree The base of the tree and the ground form a right angle as shown 13 ft 6 ft What is the distance in feet between the ground and the top of the ladder Round your answer to 2 decimal places

Round your results to two decimal places ds a c 5 5 b 4 4 a

QUESTION For each triangle check all that apply Triangle A 60 000 60d Scalene Isosceles Equilateral 60 00 EXPLANATION 7 Triangle B 11 Scalene Isosceles Equilateral 5 Triangle C Here are some common ways to classify triangles 30 Scalene Isosceles Equilateral 60 4 Triangle D 8 8 Scalene Isosceles Equilateral

Ve an EXACT answer No decimals No calculator X 60 45 12

Find the area of the figure Sides meet at right angles 5 yd 4 yd 5 yd 9 yd 10 yd yd

Find the value for z C 4 E 2 G 6 F 3 D

Find the volume of the solid below 5 cm 4 cm 6 cm 4 cm 5 cm 4 cm 3 cm

For each triangle check all that apply Triangle A 10 Oscalene Isosceles isosceles and equilateral triangles by side Equilateral 60 Triangle B 50 Scalene Lisosceles Equilateral 60 Triangle C 45 Scalene Isosceles OEquilateral 45 Triangle D 9 9 Oscalene Isosceles Equilateral 9

the triangles given have easy side lengths I am more so looking for the algebra showing the three triangles are congruent if possible The three triangles are known to be similar by A A A If the are of 3 you know same is three angles are it possible to show they side length congruent given each one

Find the volume of the solid below 5 cm 5 cm 6 cm 1 5 cm I 16 cm 5 cm 6 cm

Area of a piecewise rectangular figure Find the area of the figure Sides meet at right angles 4 m 3 m 4 m 7 m 7 m

Find the perimeter and area of the shaded figure below 1 unit 1 unit Perimeter units Area square units

Suppose is the function defined by f x Ax where a The domain of fis R4 A 6 4 3 B 0 2 1 1 C 4 0 1 1 D 0 0 1 0 E 9 0 3 F 18 4 6 6 3 9 0 1 1 2 1 3 For instance enter R 5 for R5 b The codomain off is R3 For instance enter R 5 for Rs c Select all of the vectors that are in the kernel of f You should be able to justify your answers there may be more than one correct answer 3 A 0 A 4 0 1 1 B 0 2 1 1 C 0 0 1 0 D 9 0 3 E 184 63 d Select all of the vectors that are in the image of f You should be able to justify your answers there may be more than one correct answer

Volume of a piecewise rectangular prism Find the volume of the solid below 8 cm 6 cm 11 cm 5 cm 3 cm 1 cm 3 cm S cm

At a coffee shop the first 100 customers orders were as follows Hot Small Cold 5 Medium 48 Large 12 8 5 What is the probability that a customer ordered a small given that he or she ordered a cold drink Rounded to the nearest percent 22 Enter

Find the area of the figure Sides meet at right angles 7 ft 8 ft 3 ft 5 ft 5 ft 8 ft