Geometry Questions

Verify the identity 2 tan 0 2 2 tan 0 1 tan 0 2 tan 0 2 tan 1 2 2 tan 0 tan 0

A flagpole at a right angle to the horizontal is located on a slope that makes an angle of 13 with the horizontal The flagpole casts a 14 meter shadow up the slope when the angle of elevation from tip of the shadow to the sun is 22 a Draw a triangle to represent the situation Show the known quantities on the triangle and use the variable h to indicate the height of the flagpole b Write an equation involving the unknown quantity h h 14 1 sin e Find the height of the flagpole Round your answer to two decimal places h m sin

Q is the midpoint of the line segment PR in the truss rafter shown in the figure What are the lengths of the line segments PQ QS and RS Letx 10 and y 12 Round your answer to o place QS RS

Because of prevailing winds a tree grew so that it was leaning 3 from the vertical At a point d 40 meters from the tree the angle of elevation to the top of the trees is a 26 see figure Find the heighth of the tree Round your answer to one decimal place h dm

Find the area of the triangle having the indicated angle and sides Round your answer to one decimal place C 78 15 a 12 b 24

Determine whether the Law of Sines or the Law of Cosines can be used to find another measure of the triangle a 13 b 15 C 68 O Law of Sines Law of Cosines Then solve the triangle Round your answers to four decimal places CH A 8 X xxx

A triangular parcel of ground has sides of length 750 feet 635 feet and 585 feet Find the measure of the largest angle Round your answer to one decimal place X

Find all values of 0 in the interval 0 360 that have the given function value 0 sin 8 0 12 Type an integer or a decimal Use a comma to separate answers as needed

cot 0 3 3 0 O Type your answer in degrees Use a comma to separate answers as needed

as the measure of 0 in degrees 3 2 cos 0 Express as an inverse trigonometric function 0 Type an exact answer using radicals as needed Use integers or fractions for any numbers in the expression

the acute angle that satisfies the given equation Express the answer as an inverse trigonometric function as the measure of 0 in degrees tan 0 3 Express 0 as an inverse trigonometric function 0 Type an exact answer using radicals as needed Use integers or fractions for any numbers in the expression

Given 2 similar triangles Delta ABCand Delta KJI AB 7 9 cm AC 3 8 cm BC 4 8 cm and JK 5 7 cm Construct a diagram of the triangles and determine the lengths of the unknown sides

a moving truck uses a 13 ramp to unload When the ramp is fully extended the distance between the base of the ramp and the back of the truck is 8 What is the angle of elevation

Find an equation for the indicated part of the hyperbola Lower branch of 2 2 2 2 1 25 36

Find the midpoint of points A 6 5 and B 2 4 graphically You may press submit or click the graph again to replot the midpoint Start gwer 10 9 8 7 6 5 3 2 1 10 9 8 7 6 5 3 1 1 1 2 3 4 5 6 7 8 9 10

Find the midpoint of the segment with the following endpoints 8 0 and 2 4

Prove AABC ACDA B D Given PT RT QT ST Prove APQT ARST C X C Given C is the midpoint of AE and BD Prove AABC AEDC D E Statements Statements Statements Reasons Reasons Reasons

For 2 and 3 identify all pairs of congruent corresponding parts Then write a congruence statement for the polygons 2 Corresponding Angles Corresponding Sides Congruence Statement 3 Corresponding Angles Congruence Statement 5 m M A For 8 and 9 find the values of x and y 8 ABCDEFGH 28 B 135 For 4 7 complete each statement with the correct number value given that AXYZ AMNL 4 MzY 6 mzZ 4y 4 C Corresponding Sides 7 XY D H y G 10x 65 F A N B H 142 33 9 AMNP ATUS and same L C 12 S 2x y m M 24 y R 124 Z P N 8 13 m M E 2x

K a ZLJK LLMK b mzJLM 90 c mzLKM 90 d mzLMK 90 e LJ LK f JK MK M Name 18 D EG LL a ZDFEZHGI b ZD ZH c DF HG d DE HG e DE HI f DF HG H

10 WX LV 11 WX VWXYZ Y By the 16 N LX AWXY For 12 and 13 find m21 12 L 70 N R that the polygons are congruent by filling in the blanks XY YZ VZ WV ZW XY ZU LXYW M T LX Y W LY 14 If AJKL is congruent to AXYZ then identify all pairs of congruent corresponding parts 2 LK LLE JK property WY WY LXWY 13 c ZZ ZW LZ a ZP ZR c PQ RS For 15 18 what can you conclude from the diagram Circle all correct answers may have more than 1 answer 15 X a ZX ZV b XZ VW V KL B 80 AY 45 d ZY WU W b ZN LT W d NQ ST X JL R M Y 2

a JK and KL d LP and LK a AABD ACDB B c AYXZ AWXZ W X the pair of sides given 3 Write a proof Given PQ bisects LSPT SP TP Prove ASPQ ATPQ b PK and LK e KP and PL 2 Decide whether enough information is given to prove that the triangles are congruent using SAS Congruence Theorem Explain b ALMN ANQP c KL and JL f JL and JK Statements by SAS K G N M d AEFH AGHF P Reasons

ve the general solution for the following trigonometric equation without a calculator in grees Type DNE on the larger angle if only one equation is necessary tan 48 29 1 275 Reference Angle B B degrees round to two decimal places where kZ smaller angle where kEZ larger angle

AQSU and ARST are shown below Q R S Which statement is true AQSU is similar to ARST AQSU is not similar to ARST T U There is not enough information to determine whether the triangles are similar

15 Write a program that will find the third one if you are given two out of three from the vertex centroid and midpoint For example the second screen shot shows the vertex when 4 7 and 12 2 are inputted for the centroid and midpoint NORMAL FLOAT AUTO BEAL RADIAN MP MISSING VERTEX 2 CENTROID 3 MIDPOINT NORMAL FLOAT BUTO REAL RADIAN MP GCA B MCC D A 74 B 7 C 12 D 2 12 25 Done

Select the correct answer from each drop down menu 8 8 6 2 4 2 O 6 2 4 6 8 2 4 2 60 Quadrilateral 1 and quadrilateral 2 are polygons that can be mapped onto each other using similarity transformations The transfe followed by a dilation with a scale factor of maps quadrilateral 1 onto quadrilateral 2 is a translation

a in sin b Cos SC NO c tan d cot 1 h e sec f csc g 2 sin cos 2 costan 24 0 7

Find all solutions of the equation in the interval 0 27 Use a graphing utility to graph the equation and verify the solutions cos x 1 0 X X X sin smallest value largest value

Select all the correct figures Which numbers have line symmetry 2 3 7 8

Type the correct answer in the box 2 2 Polygon 22 20 18 16 14 12 10 B 8 U 6 4 2 24 E W The figure shows five polygons ABCDE FGHIJ KLMNO PQRST and UVWXY H R 8 10 12 14 16 18 20 22 24 26 Reset cannot be mapped onto the others by similarity transformations X Next

Select the correct answer from each drop down menu LL F G E A B line segment AB ABCDEFG C There are seven lines of reflection across which the regular polygon ABCDEFG can reflect to map onto itself One of them is a of m Reset Next

A regular hexagon is rotated 360 about its center How many times does the image of the hexagon coincide with the preimage during the rotation O A OB O C O D 1 time 6 times 12 times 3 times

Which letter has point symmetry A L D

Select the correct answer What is the total number of lines of symmetry for this figure X OA 0 OB 1 O C OD 4 2

Use the half angle formulas to determine the exact values of the sine cosine and tangent expressions of the following angle 165 5 sin 165 7 cos 165 5 tan 165

The figure shows eight congruent triangles made by dividing a square that has an area of 64 cm What is the area of ABH B A O A 20 cm OB 16 cm O C 8 cm O D 6 cm OE 4 cm D H E F G

Use the product to sum formulas to write the product as a sum or difference Do not simplify your answer TT sin 8 cos 5T 6

Use the sum to product formulas to write the sum as a product 4 cos 6x 4 cos 2x

Find the exact values of sin u 2 cos u 2 and tan u 2 using the half angle formulas 3 4 3 2 U 2 tan u sin u 2 cos u 2 tan u 2

Given TU XW Prove XW 8 X 14 XW 4 7 XW 56 XW 8 Which step is missing O A O B O C O D W 7 Statements Reasons TU XW given ZUTV ZXWV alternate angles theorem ZTVU ZWVX vertical angles theorem ATVU AWVX AA U substitution property of equality cross product division property of equality Statement Statement VW Statement Statement 4 UV h Reason Corresponding sides of similar triangles are proportio Reason Corresponding sides of similar triangles are proportio Reason Corresponding sides of similar triangles are proportion Reason Corresponding sides of similar triangles are proportion

Select the correct answer Given AD BC Prove DC 6 units A 6 units D Statements AD BC ZDAC AC AC ZDCA C ZBAC DC BA DC BA DC 6 units Which step is missing given ZBCA alternate interior angles theorem reflexive property of congruence alternate interior angles theorem B O A ADAC O B ADCA O c ADCA O D ADAC Reasons CPCTC definition of congruent sides substitution property of equality ABCA by SAS ABCA by ASA ABCA by SAS ABCA by ASA

Select the correct answer from each drop down menu AABC has side lengths of 10 units 20 units and 24 units AXYZ is similar to AABC and the length of its longest side is 60 units The perimeter of AXYZ is square units 108 110 135 270 v units If the height of AABC with respect to its longest side being the base is 8 units the area of AXYZ is Reset Next

The diagram shows the lengths of corresponding sides of similar triangles A B C and ABC Which expression gives the perimeter of A B C A B a 4 CA OA 4 4 b c OB 2 a b c OC 4 a b c OD 8 a b c B 8

In the diagram the circle will be dilated by a scale factor of 3 about the origin The points C A and B map to C A and B after the dilation What is the length of C B Use the distance formula to help you decide d X X Y Y A B OC OD E 21 units 15 units 24 units 45 units 5 units 18 16 14 12 10 8 6 4 2 0 0 A 8 15 C 8 10 B 10 B 12 13 12 14 16

6 Which of these conditions might be true if polygons ABCD and KLMN are similar O A O B O C O D OE The measures of corresponding angles of ABCD and KLMN are equal but the lengths of corresponding sides of ABCD are half those of KLMN The measures of corresponding angles of ABCD and KLMN are in the ratio 1 2 but the lengths of corresponding sides of ABCD and KLMN are not proportional The lengths of corresponding sides of ABCD and KLMN are equal but the measures of corresponding angles of ABCD and KLMN are not equal The lengths of corresponding sides of ABCD and KLMN are proportional but the measures of corresponding angles of ABCD and KLMN are not equal The measures of corresponding angles of ABCD and KLMN are not proportional but the lengths of corresponding sides of ABCD and KLMN are proportional

In quadrilateral ABCD ZABC is a right angle and AB 4 units Quadrilateral ABCD is dilated by a scale factor of 2 with point B as the center of dilation resulting in the image quadrilateral A B C D Which statement is true A A B is 6 units long and lies on the same line as AB OB A B is 8 units long and lies on the same line as AB OC A B is 6 units long but lies on a different line than AB OD A B is 8 units long but lies on a different line than AB

10 A VWX and A NOP are similar If mV 44 and mP 66 what is mW OA 22 OB 33 OC 35 O D 70

Type the correct answer in the box Polygon ABCDE is reflected across the x axis to form polygon A B CDE Then polygon A B C D E is dilated by a scale factor of 0 5 about D to form polygon LMNOP Vertices A and B correspond to L and M respectively If the length of AB is 2 20 units the length of LM is units Write your answer as a decimal number to two decimal places

Quadrilateral PQRS is dilated by a scale factor of with point R as the center of dilation resulting in the image P Q R S Which statement is true about line segment P S OA OB O C OD P S 8 6 4 2 y 8 6 4 2 2 4 6 0 R Q 2 Segment P S is 4 units long and lies on the same line as segment PS Segment P S is 16 units long and lies on the same line as segment PS Segment P S is 4 units long and lies on a different line than segment PS Segment P S is 16 units long and lies on a different line than segment PS 6 0 X

rmine the rate of seepage in cubic feet sec under the dam by drawing flow net to scale ON THE DRAWING and also determine the total uplift force in psf acting at the bottom of the dam at Point B per unit length of dam The permeability of the silty sand is 5 X 10 3 ft sec The drawing is to scale K h 30 f H 40 ft A 5 ft SA 4 601 30 K 5 x 10 3 ft sec Impermeable sand 4 12

6 1 Score 2 67 46 0 21 answered Question 6 Use the given figure to answer the following The figure is not drawn to scale C a B A Find B if B 75 B D Question Help Post to forum B