2D Geometry Questions and Answers

C D 7 reflection across y 1 47 A B W T U y AY 43 43 P

8 reflection across the x axis A B D 49

6 translation x y x AYL A B C D K y

2 Point A is the midpoint MA 2x 1 and MT picture and create an equation to solve Find all MA of segment MT If 16x 22 Draw a A x 3 MA 26 C x 4 MA 9 B x 2 MA 5 D x 3 MA 7

4 Given angle IJK is bisceted by ray JE and angle IJE 4x 10 and angle IJK 6x 2 Determine the measure of angle EJK A x 9 EJK 52 C x 9 EJK 26 B x 11 EJK 34 D x 11 EJK 64

3 Find mZDRQ if mZDRQ 15x 5 m2SRD 10x 1 and mZSRO 121 e A 70 C 7 R B 92 D 62

1 Find GF A 8 C 28 18 B 30 D 9

Triangles in the Coordinate Plane When legs are vertical and horizontal directly apply the formula For right triangles with legs that are not vertical horizontal use the the base and height then use the area formula For nonright formula to calculate the box method Parallelograms in the Coordinate Plane For a set of parallel sides that are or vertical directly apply the area formula When sides are neither vertical nor horizontal use the method

S O B A The figure above not drawn to scale shows a vertical pole AB standing on horizontal ground SOA is a straight line on the horizontal ground From S and O the angle of elevation of B are 30 and 50 respectively The distance from S to B is 50 metres Calculate correct to 2 decimal places the height in metres of AB 4 marks

What is the missing statement and reason in this poof D A Statement 4 LABD LCDB Reason 5 ASA C Statement 4 LBDA LDBC Reason 5 ASA Statements 1 ABCD is a parallelogram 2 AD BC AD BC 3 DB BD 4 5 AADB ACBD B D Reasons 1 Given 2 Definition of a Parallelogram 3 Reflexive Property 4 If parallel are lines cut by a transversal create alternate interior angles are congruent 5 Statement 4 LABD LCDB Reason 5 SAS Statement 4 LBDA LDBC Reason 5 SAS

Finding the Area of a Right Triangle with Legs Parallel to the Coordinate Axes Find the area of the right triangle ABC A II 1 1 bh 00 units 36 9 h JK 4 2 2 10 A 10 8 6 4 h 10 B 512 1600 G 6 59 10 6 4 2 L 2 5 20 4 6 10 Finding the Area of a Right Triangle with Legs Not Parallel to the Coordinate Axes Find the area of the right triangle JKL d x x 1 37 b LK 4 2 2 5 U 2 10 10 2 b C A 4 13 B 10 10 K 4 2 x

Using the Box Method to Calculate the Area of a Parallelogram Find the area of parallelogram ABCD using the box method Area of rectangle 5 7 35 Area of triangles 1 Area of triangles 2 Area of parallelogram 35 Area V 4 4 3 2 2 2 6 Comparing Areas REAL WORLD CONNECTION units2 A 2 3 Find the area of the triangle using the box method A 300 2 2 1 1 1 2 3 m 10 B 7 6 5 4 3 2 99 D 5 4 3 2 1 A 12 2 2 3 The area of the parallelogram is larger by 1 square meter A L 4 3 m A The community garden has two flower garden plots available for the same price The layout is displayed on a grid where each unit equals 1 meter Based only on square meters which plot is the better purchase Find the area of the parallelogram 3 2 1 2 3 4 5 V 21 4 m h 3m 1 2 3 4 5 8 PEL 2m x 12345678910

Finding the Area of a Parallelogram in the Coordinate Plane with One Set of Sides Parallel to an Axis Find the area of the parallelogram DEFG A bh A 3 5 6 units AB 8 10 4 0 4 16 AD 210 60 1 144 36 4 2 A lw A 180 20 3600 3 5 D 3 5 3 Finding the Area of a Rectangle in the Coordinate Plane Find the area of rectangle ABCD B 2 A 10 W 6 V E 1 5 3 F5 3 G 0 3 10 4 2 ER E 24 A C D 8 10

Polygon interior angle sum theorem The sum of the measures of the LE 180 n 2 where is the number of Polygon exterior angle sum theorem The sum of the measures of the polygon one at each vertex is 360 angles of any it gon is of the polygon angles of a

A regular octagon has a radius of 15 7 ft What is the approximate area of the regular octagon rounded to the nearest tenth Step 1 Make triangles and find the interior angle measure of the polygon Step 2 Make a right triangle using an and find the angle measures of the right triangle 15 7 ft

To find the area of a rhombus or kite you can use a A d d d and d are the lengths of the diagonals F R T Derive the formula In this example the diagonals are RT and QS d HIN d T bh A Add the areas of the top and bottom triangles 1 1 A bh 2 2 2 d 2 d 2 d 2 d R Let RT 2 cm and QS 5 cm 2 5 T m S

What is the value of angle A in Clue 9 The below shape is a parallelogram Do not include degrees in your final answer k 20 A 2k 10

Find the Area of a Rhombus in the Coordinate Plane What is the area of the thombus Use the distance formula to find the lengths of the diagonals KM 14 4 2 12 232 102 102 200 2 100 LN 12 6 1 10 2 6 4 62 P 72 36 x 2 A 10 2 6 2 18 16 14 12 13 4 A 2 019 K 2 1 F 14 12 12 4 10 12 14 16 18 29

Finding the Area of a Trapezoid in the Coordinate Plane USE DISTANCE FORMULA TO FIND LENGTHS What is the area of the trapezoid d x x QT 191 5 8 RS 12 6 0 1 RU 7 6 2 7 1 DETERMINE THE AREA What is the area of the trapezoid QT 333 RS 37 RU 37 1 A h b b 1 37 333 37 A units 20 18 16 14 12 10 8 6 4 2 20 18 16 14 12 10 B 6 4 2 y Q 1 8 y U 7 7 LAT Q 1 8 1 R 6 1 S 12 0 X 24 6 8 10 12 14 16 18 20 T 19 5 U 7 7 T 19 5 R 6 1 S 12 0 x 2 4 6 8 10 12 14 16 18 20

Directions Find the value of x 7 J 31 K N M L 9 E A F 01 21x 9 C 9x 23 27 B X X 8 16x 13 p S T D R 10 Given CH bisects ZDHG mGF 2x 6 and mDC 7x 1 E 83 G X H X Gina Wilson All Things Algebra LLC 2015 2019

What is the length of x in clue Clue 8 Just write the value do NOT include x A X 15 B

Step 3 Use trigonometry to write expressions for the missing lengths Find a and b cos 22 5 a 15 7 cos 22 5 sin 22 5 h 15 7 Find the perimeter sin 22 5 P 15 7 sin 22 5 2 8 15 7 sin 22 5 16 Step 4 Find the area of the polygon 15 7 cos 22 5 15 7 sin 22 5 16 22 5 15 7 ft

D A radius of a regular polygon is a segment from the The base of the right triangle formed is half the length of the side 8 2 2 J Use the Pythagorean theorem to find a a 4 1 72 Find the perimeter Find the area cm S Q 49 4 1 a 49 4 1 P 8 2 5 49 4 14 8 2 5 8 2 cm cm to a vertex 7 cm

A regular octagon has an apothem of 12 1 inches and a perimeter of 80 inches What is the area of the octagon 12 1 80 40 12 1 in 12 1 in

Recall that a regular polygon can be broken up into congruent isosceles triangles Find the measure of each central angle 360 8 Find the measure of each base angle of the isosceles triangles 180 central angle 2 180 45 2 11 135 2 Regular Octagon 67 5 45

A 27 Which a b C d e sequence of transformations takes the graph of y k x to the graph of y Translate 1 unit to the right reflect over the x axis then scale vertically by a factor of 2 Translate 1 unit to the left scale vertically by 2 then reflect over the x axis Translate left by 2 then translate up 1 unit Scale vertically by 2 reflect over the y axis then translate up 1 unit Reflect over the line x 1 2 then translate 1 unit to the left k x 1

BA 22 100 North High students were asked about their classes this semester Are you in PE and are you in band The responses are recorded in the Venn diagram a How many students are in band b What does the number 20 represent PE 35 20

2 Classify the triangle Using une best name 130 20 7

3 Write an equation be used to solve for x given the segments A 9x 7 39 B 3x 20 C

6 Identify the center and radius of the circle given x 9 y 7 8

Find the arc length of major arc GH Round your answer to the nearest tenth 265 cm H 9 1 cm G

A 60 foot zip line from a tree to the ground forms a 45 angle of elevation from the ground How high above the ground is the top of the zip line Round your answer to the nearest tenth of a foot feet

are planting a garden in the shape of an equilateral triangle as shown in the diagram You want to find the area of the garden to determine how much topsoil will need 1 0 4 ft 4 ft A 1 2 30 4 ft ubstitute the values of b and h in the formula A b h for the area of the garden

A 20 foot ladder leans against the side of a house with its base 3 5 feet from the house Use the Pythagorean Theorem to approximate how high the ladder reaches up the side of the house Round your answer to the nearest hundredth The ladder reaches feet high

Find the length of JM JM H 20 30 K 45 M N

Rectangle A and Rectangle B are similar Rectangle A has side lengths of 10 and 15 Rectangle B has a side length of 45 What are the possible values for the length of the other side of Rectangle B Select all that apply 25 0 30 O 50 0 67 5 Previous 10 11 12 13 14 15 16 17 18 19 Next

Give the value of each trigonometric ratio cos M cos N sin M sin N tan M tan N

8 The figure is filled 20 of the way with water Determine the volume of water in the tank 9 m a 45 cubic meters b 81 cubic meters C 27 cubic meters d 120 cubic meters 9 m 5 m

You can calculate a distance across water using a surveying technique as shown in the diagram Find WX 9 52 m WX m W X 8m N 10 m Not drawn to scale

Your family has decided to put a rectangular patio in your backyard similar to the shape of your backyard Your backyard has a length of 40 feet and a width of 32 feet The length of your new patio is 14 feet Find the perimeter of your new patio The perimeter of the patio is feet

6C 13 Prove that quadrilateral ABCD is a rectangle B 4 A a qu 0 1 D M

Find the measure of ZC C B 110 m C 30 D

is the centroid of AABC What is the value of x when GD x 4 and GC 4x 5

Applying the Polygon Interior Angle Sum Theorem An internal angle of a regular polygon has a measure of 140 What type of polygon is it 180 n 2 71 and an 180 n 2 180m 360 140m 40m 360 1 The polygon is a nonagon Exterior Angles of Polygons An exterior angle of a polygon is an M of an adjacent side formed by a side of the polygon

7A 15 Quadrilateral ABCD is shown with the given angle measures Select ALL true statements A Angle A measures 140 degrees B The measure of angle A and D must add to 180 degrees C Angle A measures 55 degrees D Angle D measures 55 degrees E Angle D measures 40 degrees B C A 125 40

7A 16 Find the measure of the remaining angles of quadrilateral WXYZ X

13 A fish tank in the shape of a rectangular prism has a base with dimensions of 60 inches by 30 inches and a height of 15 inches If the tank is filled with water to a height of 7 5 inches determine the volume of water in the tank

17A 4 The arc from A to 8 NOT passing through C measures 50 degrees Select ALL the true statements A Angle BCA measures 50 degrees 8 Angle BCA measures 25 degrees C Angle BOA measures 50 degrees D The are from B to C not passing through A measures 180 degrees E Angles CBO and CAO are congruent O A

Polygons Polygons are figures formed from three or more line segments such that each segmentintersects exactly two other one at each endpoint and segments with a common endpoint are collinear concave Convex polygon Every line segment connecting any two points on the polygon itself will consistofno points outside the polygon Concave polygon The extension of at least one side or diagonal contains a point on the inside of the polygon N gon is the number of sides

A circle has a center at 4 1 and a point on the circle is located at 2 5 Write the standard form equation that would graph this circle