2D Geometry Questions and Answers

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

In the figure A B C and D are points of tangency calculate x a 20 d 36 B A 130 b 60 778 D D c 40

Determine the leading coefficient for the rational function graphed below Write as a reduced fraction with no spaces

90 B 26 26 A D C Drag the RED and GRE below Then solve the following situation algebraically on the whiteboard below ZABD and ZCBD form a linear pair and have EQUAL measure m ZABD CHF Submit

Find the value of x in the isosceles triangle shown below 80 83 8 80

If these are the degrees for the top of a hat measuring 7 5 8 I needed to know what the degrees for 7 7 1 8 7 1 4 7 3 8 7 1 2 7 5 8 7 3 4 and 8 would be So I just needed to know the degree of each angle at those measurements Hat 75 8 62 5 Degrees 55 degrees 62 5 Degrees 62 5 Degrees a 55 degrees 62 5 Degrees

Use the Pythagorean Theorem to find the value of x to the nearest tenth if necessary X 14 13

Use SOH CAH TOA to find the value of x to the nearest tenth 7 8 34

The distance from the star S to the planet X is approximately 148 700 000 kilometers km The distance from S to the planet Y is approximately 57 900 000 km The elongation angle a is the angle formed between the line of sight from X to S and the line of sight from X to Y See the figure on the right Suppose that the elongation angle is 13 Use this information to find the possible distances between X and The larger distance from X to Y is Do not round until the final answer km Then round to one decimal place as needed

11 If ARST is isosceles find mZS 15x 31 R T 9x 11 S