Geometry Questions

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

Find the area of the figure Sides meet at right angles 14 cm 7 cm 5 cm 4 cm 5 cm 5 cm 5 cm 7 cm

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

Find the value for x C 8 E x 9 G F 3x 3 4 D

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

A AC Given BC 11 mm AB 30 in in B C

Find the lengths of the diagonals of rectangle ABCD D A Xt 10 2x E ly 19 415 C B

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

A 13 foot ladder is leaning on a tree The bottom of the ladder on on the ground at a distance of 6 feet from the base of the tree The base of the tree and the ground form a right angle as shown 13 ft 6 ft What is the distance in feet between the ground and the top of the ladder Round your answer to 2 decimal places

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

QUESTION For each triangle check all that apply Triangle A 60 000 60d Scalene Isosceles Equilateral 60 00 EXPLANATION 7 Triangle B 11 Scalene Isosceles Equilateral 5 Triangle C Here are some common ways to classify triangles 30 Scalene Isosceles Equilateral 60 4 Triangle D 8 8 Scalene Isosceles Equilateral

Ve an EXACT answer No decimals No calculator X 60 45 12

Find the area of the figure Sides meet at right angles 5 yd 4 yd 5 yd 9 yd 10 yd yd

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

Find the volume of the solid below 5 cm 4 cm 6 cm 4 cm 5 cm 4 cm 3 cm

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

the triangles given have easy side lengths I am more so looking for the algebra showing the three triangles are congruent if possible The three triangles are known to be similar by A A A If the are of 3 you know same is three angles are it possible to show they side length congruent given each one

Find the volume of the solid below 5 cm 5 cm 6 cm 1 5 cm I 16 cm 5 cm 6 cm

Area of a piecewise rectangular figure Find the area of the figure Sides meet at right angles 4 m 3 m 4 m 7 m 7 m

Find the perimeter and area of the shaded figure below 1 unit 1 unit Perimeter units Area square units

Suppose is the function defined by f x Ax where a The domain of fis R4 A 6 4 3 B 0 2 1 1 C 4 0 1 1 D 0 0 1 0 E 9 0 3 F 18 4 6 6 3 9 0 1 1 2 1 3 For instance enter R 5 for R5 b The codomain off is R3 For instance enter R 5 for Rs c Select all of the vectors that are in the kernel of f You should be able to justify your answers there may be more than one correct answer 3 A 0 A 4 0 1 1 B 0 2 1 1 C 0 0 1 0 D 9 0 3 E 184 63 d Select all of the vectors that are in the image of f You should be able to justify your answers there may be more than one correct answer

Volume of a piecewise rectangular prism Find the volume of the solid below 8 cm 6 cm 11 cm 5 cm 3 cm 1 cm 3 cm S cm

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 and perimeter of the shaded figure below 1 unit 1 unit Area Perimeter square units

A rectangular paperboard measuring 20 in long and 12 in wide has a semicircle cut out of it as shown below What is the perimeter of the paperboard that remains after the semicircle is removed Use the value 3 14 for x and do not round your answer Be sure to include the correct unit in your answer 12 in 20 in in X in2 3 in

Find the area of the figure Sides meet at right angles 3 in 3 in 3 in 3 in 17 7 in 3 in 7 in 9 in

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

Refer to quadrilaterals QRST and FGHJ 13 Name a side that is consecutive with RS 14 Name the side opposite ST 15 Name a pair of consecutive vertices in quadrilateral QRST 16 Name the vertex that is opposite S 17 Name the two diagonals in quadrilateral QRST 18 Name a pair of consecutive angles in quadrilateral QRST 19 Name a diagonal in quadrilateral FGHJ 20 Name a pair of nonconsecutive sides in quadrilateral FGHJ 21 Name the angle opposite ZF R Q S Exercises 13 18 F H G

List the angles in order from least to greatest measure 9 E 10 11 X 9 cm D 15 cm 12 cm 3 0 m G 1 1m H 2 0 m 28 ft 19 ft 21 ft

24 In the diagram below of circle O tangent AB is drawn from external point B and secant BCOE and diameter AOD are drawn E B If mZOBA 36 and OC 10 what is the area of shaded sector DOE 3 1 3 10T 10 2 37 4 15

2x 20 Equation 6x 24 Angle Type Alternate Interior r S

answering the questions below 35 54 90 Triangle NYE angles of a triangle and the lengths of the sides opposite them be SQUIT F T 1380 810 Measures of the Angles mich INAY HDZF 1640 well mal 20 PU 480 FY LF LY TU QT QU MG 1030 G Lengths of Sides Opposite the Angles M

Replace each with or to make a true sentence 18 D 19 G H 20 3 E m43 m 1 75 MLG 75 K M Co m48 m26 m27

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

15 10 5 0 5 10 15 20 Exercises 12 17 Replace each with or to make a true sentence 13 HK OK 12 MT JT 14 JU OS Determine if each statement is true or false 15 MHZ JS 16 HTTM 17 KH U

Identify the angle with the greatest measure 15 K 2 3 km L 16 7 6 km 5 8 km M 19 in B J 16 in 14 in Z 17 T 6 mi R 5 mi 155 N

In the diagram below draw the two limiting parallel lines to the given line I and a point P on the Poincare model of hyperbolic geometry Indicate the two angles of parallelism for I and P

Write an equation of the line below K 8 7 6 5 4 3 2 2 8 6 S 4 2 23 6 7

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

Graph the region R bounded by the graphs of the equations Use set notation and double inequalities to describe R as a regular x region or a regular y region whichever is simpler y x3 y 3 2x x 0 Use the graphing tool to graph the region R Click to enlarge graph Describe R as a regular x region or a regular y region whichever is simpler Choose the correct answer below and fill in the answer boxes to complete your choice OA R x y h y x k y OB R x y g x y f x sys where h y x where g x and k y and f x 2 1 5 Ay 4 3 2 4 4 2 3 4 5