2D Geometry Questions and Answers

2 Reflect triangle STU across line ST Which of these is a valid reason why the image of U will coincide with J a S The image of U and J are on the same side of ST and make the same angle with it at T b The image of U and J are the same distance along the same ray from T The image of U and I will not coincide after reflection over ST d Line ST is the perpendicular bisector of the segment connecting U and J because the perpendicular bisector is determined by 2 points that are both equidistant from the endpoints of a segment C T

Given LA LC CF AD Prove AE CE 14 Steps LA LL 2 CF AD LE LE C 0 B E Reasons Given Given Identity CPCTC F

Find the missing angle measures in each isosceles trapezoid 18 O 19 J K 20 W D Z 120 M 85 Z 100 X

3 In quadrilateral EFGH HK KF and LKHE LKFG Show that quadrilateral EFGH is a parallelogram by providing a reason for each step LFKG a LEKH b AEKHAGKF c EH GF d EH GF e EFGH is a parallelogram H E K G F

0 Find the missing angles and sides in parallelogram ABCD 4 A B X 25 5 W 80 D Z C

Given CD is a median AC BC Pwove LACD LB CD 3 4 5 Steps CD is a median AC BC CD CD AACD ABCD AC BC A C Reasons Given SSS D Given Identity CPCTC B

15 X 300 Find value of x in the 30 60 90 triangle Give your answer as a simplified radical

Use the diagrams to find the missing sides of the right triangles Round your results to two decimal places as needed Figure A 5 2 6 5 a

20 60 H Find value of x and y in the 30 60 90 triangle Give your answer as a simplified radica y x

In rhombus ABCD find the missing angles A D X B C

Find the missing value 6 4 6 X

8 8 Q The length of the hypotenuse is

In rhombus ABCD find the missing angle A D X Z B C

Find the value for z 7 E 3z 1 G 2 F 2z 2 Note Solving this will result in two possible answers Always make sure the value of z produces posit lengths

Find the measures of angles A B C and D in the isosceles trapezoidl A B 2x 3y 5x 5 94

Round your results to two decimal places ds a c 5 5 b 4 4 a

Find the value for z C 4 E 2 G 6 F 3 D

For each triangle check all that apply Triangle A 10 Oscalene Isosceles isosceles and equilateral triangles by side Equilateral 60 Triangle B 50 Scalene Lisosceles Equilateral 60 Triangle C 45 Scalene Isosceles OEquilateral 45 Triangle D 9 9 Oscalene Isosceles Equilateral 9

At a coffee shop the first 100 customers orders were as follows Hot Small Cold 5 Medium 48 Large 12 8 5 What is the probability that a customer ordered a small given that he or she ordered a cold drink Rounded to the nearest percent 22 Enter

Find the area of the figure Sides meet at right angles 7 ft 8 ft 3 ft 5 ft 5 ft 8 ft

Find the area of the figure Sides meet at right angles 4 ft 5 ft 4 ft 2 ft 4 ft 2 ft 5 ft 0

Find the area of the figure Sides meet at right angles 4 m 5 m 4 m 4 m 4 m 5 m 4 m

List the sides in order from least to greatest measure 12 T 13 N 14 B S 24 137 19 38 98 445 P C 55 35

Lines BE FC and AD intersect at G Replace each with or to make a true sentence 18 m BGC 19 m BGC 20 mLAGC mLAGC mLFGE m CGE B G 43 82 to F E Exercises 18 28 D

5 The pedal triangle for AABC is obtained by joining the feet of the altitudes What happens to the pedal triangle if for example is a right angle

Determine whether each pair congruence statement and explain why the triangles are congruent 13 A 12 14 B E 15 BD

Find the surface area of the figure below to the nearest foot Be sure to label the unit 5 is the hypotenuse of the triangle I 5 ft Z fo 6 ft

In AMNP NS bisects LMNP MR bisects LNMP and PQ bisects LMPN 12 Find m24 if m23 31 13 If mLMPN 34 what is m26 14 What is m 3 if m2NMP 64 15 Find m MNP if m 1 44 16 What is m 2 if ZMNP is a right angle 17 In AXYZ YW bisects ZXYZ What is mLXYZ if m 2 62 18 Algebra In ADEF EC is an angle bisector If m CEF 2x 10 and m DEC x 25 find m DEC X Q N 3 2 O S R 12 W

H PAR 49 G Which statement best explains the relationship between lines FG and HJ O They are perpendicular because their slopes are equal O They are perpendicular because their slopes are negative reciprocals O They are not perpendicular because their slopes are equal O They are not perpendicular because their slopes are not negative reciprocals

What are the coordinates of J if the given triangle is dilated with a scale factor of 2 about the origin B 7 3 A K OJ 1 3 OJ 3 5 OJ 5 7 TULC 60

r 17 19 Use the sketch below to find each of the following 6 points 90 C ARE L AR

The circle have the same radius r while the large square is of length 1 Find the value of r up to 3 decimal places A 0 183 B 0 185 C 0 189 D 0 191

40 In the figure C is the mid point of BD LACB 50 and ZABC 90 Find LADC correct to the nearest degree A B A 23 B 25 C 28 D 31 50 C D C

A 8 OA ZA and B OB AB and BC O C ZA and C O D BC and AC C

Consider the following figure N c NP M d QS R Find the following a mZN in degrees b mzP in degrees Given AMNP AQRS mzM 69 m R 78 MN 6 QR 4 RS 7 MP 11 O S O P

What are the sides of APQR O A P Q and R OB PQ QR and PR OC None of these O D LP ZQ and ZR

What function is graphed below Oy cot Oy cot 6 4 2 6 x

13 Given LAE LC CF AD Pww AE CE D B F

3 Find m PST Q P S 11x 3 5r 9 T H

Find the area of the regular octagon below Round to the nearest centimeter Be sure to label the unit 3 cm 2 5 cm

If A B and I are collinear and AC 24 find AB and BC A 2 x 5 B X 2 C

Given AC bisects LCAB 60 Prove LDAB 120 L DAB A D C B

Given LADBE LCBD LCDB LABD Prove AABRE D ACDB A D B

Given CD is a median AC BC Prove LACD LBCD A D B

Find the supplementary angles A C 2x 30 5x10 D B LADC and LCDB

A Find x y and z if LABC ADEF 5 x E Z 11 F

2 3 Indicate three different bases for the following three congruent triangles and draw in the perpendicular height for its base on each shape Now measure in centimetres to one decimal place for each triangle the base and its corresponding perpendicular height and use the table provided to calculate the area of the triangle using the formula Area of A base X1 height A ABC Triangle Base A B C B3 A2B2C2 B1 C3 C A2 B2 Perpendicular height Area C

70 99 a Enter the values of the exterior angles for this quadrilateral in the table and calculate the sum b Drag the points to create two new quadrilaterals and complete the table for both of these c Move to the next slide and do the same for a pentagon What do you notice What do you wonder A B C Sum of Angles

Which side lengths form a right triangle Choose all answers that apply A 2 3 4 8 3 17

What other polygon do you see in the design What is the polygon with the most number of sides that you can find in this design