2D Geometry Questions and Answers

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

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

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

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

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

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

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

1 A cylindrical soup can has the dimensions shown CONDENSED Soup 17 cm 11 cm What is the surface area of the can Use 3 14 as an approximation forz Round the answer to the nearest tenth if necessar O388 6 square centimeters O 1614 7 square centimeters O777 2 square centimeters 587 2 square centimeters

If a point C is inside ZAVB then 39 23 B m ZAVB 62 OA MLAVB B m CVB C m AVC D m BVC m CVB mZAVB

ow dy X and aw dy 22 at the point w x y z 147 2 2 3 if w 3x y 3yz 3z and x Z x y 2 17

U Find X 18 10 10 All drawings are not to scale The units below are in feet 18 feet X If you cross multiply and solve for x we find that the missing length is Input your final answer in decimal form

All drawings are not to scale 2 Are the two triangles similar Similar 3 Explain the reasoning for your answer BU Font Family AA A

All drawings are not to scale The units below are in feet 10 20 20 8 View this drawing as 2 triangles one inside the other The corresponding angles are meaning that all of the sides should be pro Input your answers WITHOUT spaces 9 If you cross multiply and solve for x we find that the missing length is

For the equations below determine A If the parabola opens up down left or right B The vertex of the parabola C The location of the focus D The equation of the directrix E The equation of the axis of symmetry 1 x 5 1 40 y 5 2 x 8 1 44 y 1 3 x 8 1 28 y 9 4 x 3 1 16 y 4 5 y 9 1 12 x 7 6 y 1 1 4 x 2 7 x 4 1 4 y 3 8 y 2 1 8 x 4 9 y 5 1 12 x 4

7 If two things are equal and an amount is add to one side the equation must E balanced by adding the same amount to the other side of the equation Symmetric Property Reflexive Property Transitive Property Additive Property is property W AAA FE E

X z 10 Mr F likes Pizza Ms Diaz and Mr F like the same thing Ms Diaz likes 11 19 x 19

e an algebraic example i Font Far Symmetric E Reflexive Pr Transitive P Additive Pro

2 Rotate the figure 180 clockwise O

10 In AABC M and N are the midpoints of AB and BC respectively MN x 5 AC x 2x 5 Find x MN AC 2 points C A M N B

11 In trapezoid ABCD with AB DC M and N are the midpoints of AD and BC 2 points respectively AB 4x 9 DC 6x 3 and MN 3x 4 Find x MN AB DC A B D M X N MN C

6 In ABCD AB 2x 7 BC 3x 4 and CD 3x 2 Find x and DA 2 points D B C

4 Given ABCD m A 2x 3 and m B 3x 23 Find the measure of ZA and ZB 2 points A D B C

3 Use the given information to state the reason why AADC ABDC a ZA ZB AC BC AD BD b ZA ZB AD BD 41 42 a b 1 point each A 12 D B

a Similarity Question 1 Select one BE In the figure above which of the following would allow you to prove A CBA similar to A EDA O DA CB ZDEA ZA A ZC LA

11 Find the sum of the measures of the exterior angles of a an equilateral triangle b a rectangle each interior angle is a right angle

3 Find the measure of each exterior angle of a regular polygon of n sides if a n 4 b n 12

29 Given Prove Plan R Parallelogram RSTV also XY VT 21 LS First show that RSYX is a parallelogram S

In Exercises 19 to 22 classify each statement as true or false In Exercises 19 and 20 recall that the symbol C means is a subset of 19 Where Q quadrilaterals and P polygons QCP 20 Where Q OCP quadrilaterals and P parallelograms

3 MNPQ is a and m M 110 Find a QP b NP parallelogram Suppose that MQ M P N c mZQ d m P 5 MN

11 Given that mA 2x 3 and m B 3x 23 find the measure of each angle of ABCD

In Exercises 27 to 30 use the definition of a parallelogram to complete each proof 27 Given Prove R V 1 RS VT 2 3 4 RS VT RV 1 VT and ST VT RSTV is a parallelogram Statements S PROOF Reasons 1 2 Given 3 If two lines are to the same line they are to each other 4 If both pairs of opposite sides of a quadrilateral are II the quadrilateral is a

9 Given that AB 3x 2 BC CD 5x A D 4x 1 and 2 find the length of each side of ABCD B Exercises 9 16 C

For Exercises 5 to 8 MNPQ is a parallelogram with diagonals QN and MP 7 8 M Exercises 5 8 5 a If QN 12 8 find QR a If QR 7 3 find RN If QR R If MR and MP N b If MR 5 3 find MP b If MP 10 6 find RP 2x 3 and RN x 7 find QR RN and QN 5 a 7 and MP 12a 34 find MR RP

In Exercises 17 and 18 consider RSTV with VX 1 RS and VY I ST 17 a Which line segment is the altitude of RSTV with respect to base ST b Which number is the height of RSTV with respect to base ST 18 a Which line segment is the altitude of RSTV with respect to base RS R 12 20 b Which number is the Exercises 17 18 height of RSTV with respect to base RS 16 15

26 Quadrilateral RSTV has RS TV and RS TV Using intuition what type of quadrilateral is RSTV R S