Geometry Questions

Find the measure of 0 in the triangle Do not use a calculator 0 3 2 3 3

Find the following b if A 27 3 and c 5 kht Srove to C B a

3 The triangle is inscribed in the circle below Find x 5 units

7 Find x units 24 8 Explain the logic process you when through to arrive at your answer A What properties did you use B What formulas did you use

1 Find x units 2 Explain the logic process you when through to arrive at your A What properties did you use B Wat formulas did you use

22 In trapezoid RSTV RV ST m SRV 90 and M and N are R midpoints of the nonparallel sides a What type of triangle is ARMN b If ST 13 RV 17 and RS 16 how long is RN c What type of triangle is ARVN HINT Use lengths of sides found in part b M S T N

19 In isosceles trapezoid WXYZ with bases ZY and WX 10 and ZY 8 YX WX 20 Find height h the length of ZD or YE 20 In trapezoid WXYZ with bases ZY and WX ZY 12 YX 10 WZ 17 and W N D Exercises 19 20 Y E X

5 Given isosceles trapezoid ABCD find a AC if BD 12 3 cm b x if AC 3 x 7 and BD A B D C 9 x 6

A D 18 Given E Exercises 17 18 Prove C B Isosceles AABE with AE BE also D and are midpoints of AE and BE respectively ABCD is an isosceles trapezoid

17 Given Prove A D E ABCD is an isosceles trapezoid AABE is isosceles C B

25 In the figure a b c and B is the midpoint of AC If AB 2x 3 BC x 7 and DE 3x 2 find the length of EF 26 In the figure a b c and B is the midpoint of AC If AB 2x 3y a b A B C E FL

In Exercises 11 to 16 the drawing shows trapezoid ABCD with AB DC also M and N are midpoints of AD and BC respectively M A Exercises 11 16 11 Given Find 12 Given Find B N AB 7 3 and DC 12 1 MN MN 6 3 and DC AB 7 5

K Exercises 7 8 8 If LH and LJ are supplementary in HJKL are a ZK and LL necessarily supplementary also b LH and ZK necessarily supplementary

5 If the diagonals of a parallelogram are perpendicular and congruent what can you conclude regarding the parallelogram

1 Being as specific as possible name the type of quadrilatera that a has four congruent sides

In Exercises 11 to 14 considerMNPQ with diagonals MP and NQ When the answer is not a whole number leave a square root answer 11 If MQ 6 and MN 8 find NQ and MP 12 If QP 9 and NP find NQ and MP 6 13 If NP 7 and MP 11 find QP and MN M Exercises 11 14 N P

In Exercises 8 to 10 use the properties of rectangles to solve each problem Rectangle ABCD is shown in the figure A B Exercises 8 10 8 Given Find 9 Given Find D C AB 12 5 and BC CD AD and AC not shown AB 2x 7 BC CD 3x 2 x and DA 3x 4 and

3 Being as specific as possible name the type of parallelogram that a has congruent diagonals b has perpendicular diagonals

2 For the given model of the form x a Determine the value of p b Identify the focus of the parabola c Write an equation for the directrix Express numbers in exact simplest form x 4y 2 Part 0 3 4py Part 1 of 3

Find 30 Given Find 31 Given Find y MN and ST MN x 5 ST x MN and ST X x 2x 5 RM RN ST 5x 3 m R 60 x RM and ST 2x 1 R M N S Exercises 29 31

5 Consider any kite a Does it have line symmetry If so describe an axis of symmetry b Does it have point symmetry If so describe the point of symmetry

Z W X Exercises 3 4 4 In the drawing suppose that ZX is the perpendicul bisector of WY What type of quadrilateral is WXY

7 In parallelogram ABCD not shown AB 8 m B 5 Which diagonal has the greater length and BC 110

S X Y N T Exercises 11 14 12 If XY 6 YZ 8 and XZ 10 find a RS b ST c RT 13 If the perimeter sum of the lengths of all three sides of ARST is 20 what is the perimeter of AXYZ

a As shown must RSTV be a parallelogram b With measures as shown is it necessary that RS 5 V 8 T

5 A carpenter joins four boards of lengths 6 ft 6 ft 4 ft an 4 ft in that order to form quadrilateral ABCD as shown a What type of quadrilateral is formed b How are angles B and D related B A 6 6 D 4 C

In Exercises 11 to 14 assume that X Y and Z are midpoints of the sides of ARST 11 If RS 12 ST a XY S X R Y 14 and RT 16 find b XZ N T c YZ

20 Given Prove 1 2 Draw AC Quadrilateral ABCD with midpoints E F G and H of the sides EF HG Statements 4 PROOF 3 In AABC EF AC and in AADC HG AC D H A G Reasons E C 1 Given 2 Through two points there is one line 3 4 If two lines are to the same line these lines are UL B

A M N B Exercises 9 10 10 In ABC M and N are midpoints of AC and BC respectively If MN 7 65 how long is AB

D E NNM B F A C Journal Proofs of Congruence 6 7 2 5 3 Copyright 2023 Apex Learning Inc Use of this material is subject to Apex Learning s Terms of Use Any uthorized conving reuse or redistribution is prohibited

Use the elimination method to find a general solution for the given linear system where differentiation is with respec L x 6x 10y sint y 5x 4y cost Eliminate x and solve the remaining differential equation for y Choose the correct answer below 162 A y t C 2 cos 5t C esin 5t cost 629 162 OB y t C e C te cost 629 OC y t C e cos 5t C sin St 138 629 162 E y t C e Cate cost 000 162 629 sint 138 630 cost 162 OD y t C e cos 5t C sin 5t cost 629 GILB sint 138 629 138 629 sin t sint 138 629 sint

7 Why do you think triangular structures are so stable 2 points

6 Are the truss triangles AADB and ABFC congruent Which postulate did you use for your proof Which engineer was correct 1 point

1 0 1 2 3 4 5 1 2 V 3 4 4 3 L D 5

3 Here is a picture of the bridge truss and the given information 1 AC DF 2 E is the midpoint of DF 3 B is the midpoint of AC 4 EBAC Fill out the two column proof to prove that ABED ABEF You B may not need to use all the rows 5

4 State how you know that ABDF is an isosceles triangle 2 points

Given the system of equations 2x 3y9z 16 x 3z 4 3x y 4z 4 a determine whether the system is inconsistent or dependent Your answer is input inconsistent or dependent dependent b if your answer is dependent in a find the complete solution Write x and y as functions of x

State the property or properties used to rewrite each expression log 3x log log 3x

Find the exact value of sen a if a 3 and b 5 03 34 3 3 34 34 03 34 34 O 34 3 34

1 Convert each of the following angles to radians There are some negatives a 30 b 45 c 210 e 120 g 150 1 90 k 240 d 225 f 135 h 180 1 60 1 270

Complete the statement below If z 625 cos 120 i sin 120 then any fourth root of z has r and the fourth root with least positive argument h

8 Drag the movable black point to set the left vertical asymptote and shift the function the red point to set the right vertical asymptote thereby setting the period of the function and the blue point at the correct set of coordinates You may click on a point to verify its coordinates Note that the two asymptotes can be moved independently of each other and that only one period of the function is shown Provide your answer below TT 5t 42 3 2 4 1 0 0 2 1 1 2 0 f 2TT 3TT 4 4TT 5TT

Drag either of the movable red points to set the asymptotes for one period of the given function Also place the blue point at the correct set of coordinates You may click on a point to verify its coordinates Provide your answer below TT 2 3 8 TT 4 TT 8 7 6 5 4 3 2 1 10 1 2 3 4 5 6 TT 8 TT 4 31 8 TT 2

B 12 9 D Are the triangles similar C 3 D B

Determine the area of the triangle with vertices 10 4 0 11 1 1 and 11 4 4 Use the square root symbol where needed to give an ex ct value for your answer Area 0 o G Determine the area of the triangle with vertices 10 4 0 11 1 1 and 11 4 4 Use the square root symbol where needed to give an ex ct value for your answer

Write an equation of the graph given below 21 Provide your answer below 1 0 2 0 1T1 3 TT 2 3 TT 3 4 31 4 nin n TT

y 3 cos 1 Drag the black dot to shift your graph in the desired direction Use the blue draggable dot to change the period Drag the orange dot to change the amplitude and or reflect with respect to the x axis The horizontal distance between the vertica dotted green lines corresponds to one period Provide your answer below 2T 54 A 3 NI 0 1 0 1 2TT 4 1

Find the surface area of the triangular prism O615 m 676 m O 511 m 451 m 15 m 13 m 11 m 15 m

1 2 3 4 14 9 ft 15 1 ft 5 8 m 13 7 ft 14 9 ft 6 m 15 1 ft 2x 5 6x 11 5 m 6 m 2x 13 x 14 5 8 m 4x 9 x 6 X 4 3x 1

John left a scavenger hunt for his friends He advised his friends to travel 5 blocks west and 3 blocks north Which translation rule below describes John instructions x y x y x y x y x 3 y 5 3 y 5 x 5 y 3 5 y 3