2D Geometry Questions and Answers

A town s population is currently 20 000 If the population doubles every 34 years what will the population be 68 years from now

A growing farming conglomerate increases its water usage at a rate of 10 every year If it used 13 000 megaliters of water this year then how much water will it use 17 years from now If necessary round your answer to the nearest hundredth

Richmond County has a population of 850 000 people which increases by 10 every year due to a growing tech industry What will the population be in 2 years If necessary round your answer to the nearest whole number people

Choose ALL answers that describe the quadrilateral HIJK if diagonals HJ and IK intersect at point L HL LJ and IL LK Parallelogram Rectangle Rhombus O Square O Trapezoid

A B H G my iPhone K C F D E

The actual charge was 38 as shown in the graph Drag the red points to fit the line to the data Do you think a linear model is an appropriate choice here Yes No A

5 Jill Wilson uses her vehicle primarily for pleasure She has 100 300 bodily injury and 50 000 property damage coverage Because of her excellent driving record her driver rating factor is 1 00 Her vehicle is classified as A 14 Free business

The distance from home to school is 200 feet and from school to the athletic field is 150 feet What is a possible distance in feet from the athletic field to home diagram not drawn to scale Home O 00000 School 71 85 93 107 133 215 You must select all correct answers for full credit 34 42 49 60 280 298 349 350 370 GU 20 MERE BASHS SE 400 BAIE 1635 Athletic field

5 A quadrilateral ABCD can be drawn to represent an open space in a new development Remember that the vertices are listed in order as you walk around the outside of the quadrilateral Angles A and C are right angles Angle B measures 110 Side AB measures 25 meters and side BC measures 32 meters a Follow steps similar to activity 4 to make a scale drawing of this open space b How long are sides CD and AD on the open space What is the measure of angle D

4 Which is true about this trinalge A 0 0 0 100 55 AC BC AB BC AB BC AB AC AC BC AC AB 1 point The new soccer coach told her team to run from one corner of the field to the other Based or the measurement below approximately how far will the team have to run 110 yards B 125 yards 170 yards 135 yards 60 yards

D A hexagon is a six sided polygon What do you think the sum of the measures of the angles in any hexagon is Test your conjecture by drawing any hexagon and measuring the angles lts from activities 7 10

8 Triangle MNT has the following measurements ZM 45 21 75 a Make a rough sketch of this triangle b Use your ruler and protractor to carefully draw the triangle c Determine the area of your triangle You may need to make additional measurements d Determine the perimeter of your triangle You may need to make additiona measurements MT 6 4 cm

Name all similar triangles to triangle CDE A w C 55 15 90 F 17 B D

Segment VU is parallel to segment LM Find the missing length L V M24 U 44 27 24 11 8 N

AL B 1 6m 1 2m A ramp is prism shown 95 Find the length Find DCE

2 1 3 5 2 22 23 3 23 24 4 21 24 6 1 21 and 22 are complementary 2 mz1 m22 V Given 21 and 22 are complementary Prove XA1 XC 3 mz AXC mz1 mz2 4 mz AXC 5 ZAXC is a right angle 3 4 Skip this step 4 1 2 3 VI Given 21 and 22 are supplementary Prove 23 and 24 are supplementary 4 5 6 1 Given 2 Def of supplementary angles 3 Vertical angles are congruent 4 Def of congruent angles 5 Substitution 6 Def of

Describe and graph the set of points that satisfies the given equation in R xyz space x 2 2 z 5 2 4

Graph the image of the figure using the transformation given 1 translation 2 3 3 reflection across the y axis 5 translation r y 5 4 2 translation 4 5 4 reflection across the x axis 6 translation x y x y 4

Write the equation from the following table BE SURE TO IDENTIFY THE SLOPE AND Y INTERCEPT X 3 0 3 6 y 3 1 5 9

Normal Find the x and y intercepts for the equation BE SURE TO WRITE AS COORDINATE POINTS 12x 6y 108

7 Trapezoid ABCD has the following measurements The bases are AD and BC ZA 67 AD 10 4 cm D 90 DC 5 0 cm a Make a rough sketch of this trapezoid The bases of a trapezoid are the parallel sides b Use your ruler and protractor to carefully draw trapezoid ABCD Measure sides AB and BC and ZB

Solve for x The pair of polygons are similar 60 10x 21 O 12 O 14 110 O 17 54

yard is at point B with the top of the tree at point C Sue stand so her shadow meets the end of the tree s shadow a point A A 5 ft 8 ft D Question 4 24 ft B What is the ratio of the triangles 1 p

The two polygons are similar Find the measure of angle E A 6 12 70 50 90 60 B 75 D E None of the other answers are correct H 125 G

Triangles ABC and EDC are similar Find the measure of angle D 62 B O 62 O 61 O 67 O 60 610 D E

The two polygons are similar Find the values of x and y X y 22 60 18 W x 4 12

Solve for x The pair of polygons are similar 5x 5 B O 15 The scale factor from A to B is 9 10 O 18 O 19 A O22 72

The two polygons shown are similar Calculate the value of OK M OK ok H R 17 12 75 S

A passenger in an airplane flying at an altitude of 12 miles sees two towns directly to the left of the plane The angles of depression to the towns are 26 and 45 How far apart are the towns Round to two decimal places as needed Show your work here

In parallelogram DEFG DH x 3 HF 3y GH 4x 5 and HE 2y 3 Find the values of x and y The layan G OA OB OC OD x H R 2 y 3 x 6 y 3 x 3 y 2 x 3 y 6

For the parallelogram if m42 5x 28 and m44 3x 10 find m43 The diagram is not to scale OA 163 OB 17 173 9 C D 1

Classify the quadrilateral OA square OB parallelogram OC rhombus OD trapezoid

Three angles in a quadrilateral measure 54 25 and 99 What is the measure of the fourth angle OA 2 OB 92 C 182 272

For a triangle list the respective names of the points of concurrency C perpendicular bisectors of the sides bisectors of the angles medians lines containing the altitudes A circumcenter incenter orthocenter centroid OB OC OD circumcenter incenter centroid orthocenter incenter circumcenter orthocenter centroid incenter circumcenter centroid orthocenter

The OA incenter OB circumcenter OC median OD concurrent of a triangle is a segment whose endpoints are a vertex and the midpoint of the opposite side

3 and M are base angles of isosceles trapezoid JKLM If m43 20x 9 and m M 14x 15 find m K OA 151 OB C 1 29 75 5

Find the length of segment AB given that segment DB is a median of the triangle and AC 26 B OA 26 OB 52 OC Not enough information is given OD 13

Find the center of the circle that you can circumscribe about the triangle A 4 1 5 c 4 3 OA OB OC D B 2 3 0 1 21 13 0 2 1 1 4 5 X

One side of a kite is 8 cm less than four times the length of another side The perimeter of the kite is 78 cm Find the lengths of the sides of the kite DA 9 4 cm and 29 6 cm OB 23 5 cm and 86 cm OC 23 5 cm OD 9 4 cm

Name the median for AQRS OA B OC QV RT QT SU

MO bisects LLMN m LM0 8x 23 and m NMO 2x 37 Solve for x and find m LMN The diagram is not to scale OA OB OC SOD x 9 m LMN 98 x 9 m LMN 49 x 10 m LMN 114 x 10 m LMN 57 L 0 M N

6 For which situation could you prove A1 A2 using the HL Theorem I 2 OA I only OB I and II OC II and III OD II only II 4 8 III 2

MO bisects LMN m LMN 5x 23 and m4LMO x 32 Find m NMO The diagram is not to scale L OA OB C D 66 45 75 61 29 M N

Find the value of x The diagram is not to scale 48

1 The triangles CER and LUR are C E R OA Congruent by HL OB Congruent by SAS OC Congruent by AAS OD Not necessarily congruent

Given XY ZW and ZY WX State which postulate or theorem you can use to prove that the triangles are congruent How can you use this to prove that Y W W Z OA AAS Corresponding parts of congruent triangles are congruent OB ASA Corresponding parts of congruent triangles are congruent OC SSS Corresponding parts of congruent triangles are congruent OD SAS Corresponding parts of congruent triangles are congruent

The triangles below are congruent by A A SAS AAS HL

3 What other information do you need in order to prove the triangles congruent using the SAS Congruence Postulate B C D OA ZBAC ELDAC OB AB AD C AB AD D LCBA LCDA 2

Use the information in the figure 2D measures D 116 E F Drawing not to scale degrees

The triangles are congruent by the AABD ACBD B congruence theorem SSS SAS ASA