Geometry Questions

Ques estion The two angles of a triangle ABC are 45 and 66 and the measure of the side containing these two angles is 3 cm Find the measure of the third angle O 69 90 O 111 180

Question 7 Points 3 Find the translation rule and the scale factor of the dilation by transforming the circle C to C AY 10 9 8 7 6 5 4 3 2 1 10 9 8 7 6 5 4 3 2 1 2 3 5 6 7 8 9 10 C 1 2 3 4 5 6 7 8 9 10 Translation 11 units to the right and 8 units up Scale factor enlargement ratio 4 Translation 7 units to the left and 11 units down Scale factor reduction ratio 1 3 Translation 11 units to the right and 7 units up Scale factor enlargement ratio 3 Rese Reset after asses R Ques 1 3 5 7 9

Question 5 Points 2 Find the translation rule by transforming a circle C with center 2 5 of radius 3 units to circle C with center 3 3 of radius 6 units when C is transformed to C Translation x y x 5 y 8 O Translation x y x 5 y 8 O Translation x y x 5 y 8 O Translation x y x 5 y 3

Question 8 Points 1 Find the measure of the angle C in the triangle A 45 12 C O 75 90 O 105 O 150 C a 30 B

Question 3 Points 1 Which of the following is true about the scale factor of dilation O It is the ratio of corresponding angles It is the ratio of corresponding side lengths O It is the product of corresponding angles OIt is the product of corresponding side lengths

Find the translation rule and the scale factor of the dilation by transforming the circle R to R 101Y 10 R 19 6 4 2 20 2 4 R 10 2 6 X 10 Translation x y x 7 y 8 Scale factor 3 Translation x y x 7 y 8 Scale factor 4 Translation x y x 7 y 8 Scale factor 3 Translation x y x 7 y 8 Scale factor 4

Question 1 15 Points 3 Find the transformation transforming the circle C to C 10 5 20 15 10 5 0 C 5 y rule and scale factor in C2 5 10 X 15 O Translation x y x 5 y 16 and scale factor O Translation x y x 5 y 16 and scale factor Translation x y x 5 y 16 and scale factor

Which of the following statement is true O The value of it is same for all circles O The value of it is different for similar circles O The value of is same for all congruent circles O The value of is a negative number

A farmer wants to put up fencing around his rectangular field to keep his cows from grazing the growing plants 1 If the length of the field is 300 ft and the width is half of the length find the perimeter of the field Field Perimeter ft 2 If each fence consists of 5 individual strands of wire attached to a post positioned every 10 feet A How many fence posts are needed B How many feet of wire is needed posts ft of wire

10 The length of a rectangle is twice the width If the width is 9 feet find the perimeter ft

11 Find the perimeter of the parallelogram if one set of parallel edges is 10 2 feet and the other set of parallel edges is 4 8 feet

3 Find the perimeter of a square whose side is 10mm Perimeter mm

The accompanying data gives the results of a survey on the number of hours spent online per week on a certain social networking website Determine if the mean number of hours spent online per week is the same for males as it is for females Assume that the population variances are unequal Click the icon to view the social media survey data Is there sufficient evidence at the 0 05 level of significance that the mean number of hours spent online per week is the same for males as it is for females Determine the null hypothesis Ho and the alternative hypothesis H Let females be population 1 and males be population 2 Ho H Type integers or decimals Do not round b 2 Female 3 Female 4 Female 5 Female 6 Female 7 Female 8 Female 9 Female 10 Female 11 Female 12 Female 13 Female 14 Female 15 Female 16 Female 17 Female 18 Female 19 Female 20 Female 21 Female 22 23 Gender 4 Male 9 Male 8 Male 5 Male 7 Male 12 Male 1 Male 6 Male 2 Male 5 Male 8 Male 13 3 7 3 8 5 Male 4 Male 6 8 Hours online week 6 14 6 4 6 4 9 3 7 8 6 4 4

5 Rewrite the following statement as a conditional statement Rick s electricity was turned off because he forgot to send in his payment O If the electricity gets turned off then Rick forgot to send in his payment O If Rick forgot to send in his payment then his electricity is turned off O If Rick s electricity is not turned off then he didn t forget to send in the payment O If Rick didn t forget to send in the payment then his electricity didn t get turned off

2 Write the converse of the statement If it is raining then I will not go to school If I don t go to school then it is raining If I go to school then it is not raining If it is not raining the I will go to school O If it is raining the I will go to school

4 Determine if the following statement is valid or invalid You live in California if and only if you are an American O Valid O Invalid

3 Rewrite the following statement as a conditional statement Jim didn t study for his test so he failed the class O If Jim did not fail his class then he studied for his test If Jim fails his class then he didn t study for his test If Jim studies for his test then he will not fail the class Olf Jim doesn t study for his test then he will fail the class

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