Geometry Questions

19 K IJ A SU C UT AUTS B TS D ZU T S

20 ALMN AQRS L M ZN A ZS C SQ N 2 B ZR D ZQ R

13 reflection across y x E 3 2 D 4 3 C 2 4 B 0 2 A D 0 3 C 2 4 B 4 2 E 1 2 B D 3 4 C 4 2 B 2 0 E 2 3 C D 3 4 C 4 2 B 2 0 E 2 3 P D 4 3 C 2 4 B 0 2 E 3 2 formation

16 G A rotation 90 clockwise about the origi B translation 2 units right and 5 units u C rotation 180 about the origin reflection across y x

12 rotation 90 clockwise about the origin D 2 4 C 2 5 B 3 5 A 2 1 A D 2 4 C 2 5 B 3 5 A 2 1 B D14 2 C 5 2 B 5 3 A 1 2 C D 4 2 C 5 2 B 5 3 4 1 2 D D 0 0 C 0 1 B 5 1 A 4 3

14 W V W X X X A rotation 90 clockwise about the origin B translation 2 units right and 6 units up C reflection across x 1 D translation 7 units right

1 translation 1 unit right and 1 unit up D 2 3 E 3 2 F 2 1 G 3 4 A D 0 1 E 1 4 F 4 3 G 5 2 B D 3 1 E 4 4 F 1 3 G 2 2 C D 1 2 E 2 3 F 3 2 G 4 3 D D 2 4 E 3 1 F 2 0 G 3 5

The graph of y f x is shown as a red dashed curve with the points A B C and D highlighted Draw the graph of y f x by dragging the blue movable points to the transformed locations of A B C and D Provide your answer below 10 5 10 5 0 5 1 1 1 VA 5 B D 10

C H B A 9 rotation 90 counterclockwise about the origin H 421 H G

D 10 rotation 180 about the origin A B F F Ay G y x

f x is shown in blue Draw the graph of y 2f x shown in red by determining how a stretch or compression will transform the location of the indicated blue points Drag the movable red points to the desired coordinates Provide your answer below 104 9 8 8 7 2 6 3 4 9 5

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

GH is tangent to circle F at point L Find mZGLK 124 58 mZGLK Type an integer or a decimal Do not include the degree symbol in your answer Q

Simplify and write the trigonometric expression as a single trig function sin x cotx cos x Cusmanl

If 0 following 5T 4 sec 0 equals 2 csc 0 equals tan 0 equals then find exact values for the cot 0 equals o

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 center of Clue 18 Input your answer as a coordinate point x y with no spaces A Identify the center of the circle with the equation shown below x 6x y 4y 7

Use 3 14 for pi and round your answer to the nearest tenth Clue 17 What is the volume of this sphere Use 3 14 for T Round yo answer to the nearest tenth 11 cm cm

Based on appearance which names correctly classify this figure Choose ALL that apply Enter capital letters in alphabetical order into the lock A rectangle B square C kite D rhombus E parallelogram F trapezoid

What type of triangle is shown in Clue 15 Classify the triangle by its best name only entering scalene isosceles equilateral or right triangle in the text box starting with a capital letter 8x 1 3x 4

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

What is the missing reason in this proof Use SAS SSS or ASA E H Statements E is the midpoint of DF DJ FH EJEH DE FE ADEJ AFEH Reasons Given Given Given Definition of Midpoint

DETERMINE THE AREA Find the area of the right triangle JKL LK 45 JK V180 36 bh 1 1 0 180 HIN V8100 90 units A1 5 10 42 2 2 6 3 0089 Area of A ABC 60 25 6 4 I 2 10 10 6 A V L 2 5 5 4 3 3 S 10 GY 6 10 1122 6 Finding the Area of a Nonright Triangle Using the Box Method Find the area of triangle ABC by finding the area of the bounding box and subtracting the areas of the right triangles surrounding triangle ABC a 52 11s 6 K 4 2 B 3 3 10 4 SS

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

he Height of a Parallelogram What is the perpendicular distance between the line segments AB and CD if the area of parallelogram ABCD is 165 square units 10 b AB 225 VB 0 10 10 6 Q 10 F A 165 AB a D 3 4 C 138 AB 0 9 10 2 9 123 165 15 a units 10

What is m BCD B 92 O C D 126 m BCD

What is the value of x in Clue 11 Enter the numeric value for x only rounded to the nearest tenth 6x 15 4x

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

equal siope intercept form do not include any spaces in the equation Write the equation of a line perpendicular to 2x 5y 10 that passes through 10 3

To find the area of a rhombus or 1 use the Tormula H 1 201 0 To find the length of a segment you can use the d x x y 11 use the formula A d d formula

1 Directions Find the following arc measures J 3 5 0 127 G F N K D 104 K L L M E 67 This is M mJL mJML mDE mFE mDEF mCFD mDFE II 2 page mKL mLON mOM mKNL mNL 2 4 U 44 T Y 55 X U A D 164 B C V Z 108 S R 25 W mBC mABC mTQ mQR mTS mSQR mRQT II mXVW mVW mYWU II mYU mXW

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

A formula for the area of a regular polygon is A 2 length HE a is the where p is the To find missing lengths draw a Then use the Pythagorean theorem or trigonometric ratios triangle using a radius and apothem

Finding the Perimeter of a Trapezoid in the Coordinate Plane What is the perimeter of the trapezoid with vertices B 4 4 C 11 4 D 20 10 and E 4 10 Round to the nearest tenth Find CD Find the perimeter 20 18 16 14 12 10 8 6 4 2 CD 2011 2 10 4 81 36 V 2 E B 4 6 P 81 36 29 P B C units 10 12 14 D 16 18 20 X

Finding the Area of a Trapezoid To find the area of a trapezoid you can use a h b b 5 6 9 units D b b 6

Finding the Area of a Trapezoid in the Coordinate Plane Using the Box Method What is the area of the trapezoid Area of rectangle B L 12 10 Area of triangle 1 6 12 Area of triangle 2 100 Area of triangle 3 2 4 8 Area of trapezoid 120 36 8 16 20 1 18 16 14 12 10 8 6 17 2 6 x 4 N Draw the box around the trapezoid and label triangles 1 2 and 3 2 41 6 units Finding an Unknown Side Length The area of a trapezoid is 86 86 square inches The height is 17 2 inches and one base is 6 inches What is the length of the other base 1 h d b A 17 2 6 x 173 72 X 8 10 12 14 16 18 20

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