Geometry Questions

A steep mountain is inclined 68 from the horizontal and rises to a height of 3200 ft above the surrounding plain A cable car is to be installed running from a point 930 ft from the base of the mountain to the top of the mountain The shortest length of cable places You can round the distance from the top of the mountain to its base to 5 3 additional decimal places or use the Ans feature on your calculator ft Round the final answer to 2 decimal

3 Solve for x 5 20 IM2 20 22 Kuta Software LL C Test Similarity Find the missing length indicated 1 K X 16 10 25 4x 2 x 8 10 5 X 8 16 5 CX 8 12x 48 12 12 x 4 1 25 12 tho 10 5X 40 16 27 30 X 4875 145 91 40 Kate Spia 120 AT Ale 50F5X XE S rights reserved 3 SASCH 2 4 6 Name Guisom Ahmadal 4x y V 4 20 34 15 15 GX 35X 8e 35 21 9x 2 20 9x 2 12 25x 296 25 25 X 8 225 904x41 255 36X19 15 Period 20 21x3c9x 2 21 54 12 321 54 32 X 6 216 36x 36 36 35 140 20x 20 20

A bag contains eight red marbles and four blue marbles You randomly pick a marble and then pick a second marble without returning the marbles to the bag The first marble is red and the second marble is blue Determine if this scenario involves independent or dependent events O Independent Events

one marble from the jar After you put that marble back in the jar you randomly draw a second marble Use this information to answer the questions Round your answers to the nearest tenth of a percent Do NOT include the percent symbol Question 7 2 pts What is the probability that you draw a blue marble first and a red marble second Question 8 2 pts

answers to the nearest tenth of a percent Do NOT include the percent symbol Question 9 2 pts What is the probability that the spinner stops on purple first and red second Question 10 2 pts

There are 4 green 10 red and 6 yellow marbles in a bag You choose a marble without looking put it aside and choose another marble without looking Find the probability that you choose a red marble followed by a yellow marble Express all probabilities as simplified fractions

A bag holds 4 white marbles and 2 blue marbles You choose a marble without looking put it aside and choose another marble without looking Find the probability that you choose a white marble followed by a blue marble Express all probabilities as simplified fractions

A die has the numbers 3 5 6 8 10 and 12 on its faces You roll the die twice What is the probability that you roll an odd number on both rolls Enter your answer as a simplified fraction

4 5 9 CHAPTER 12 Find the volume of the figure Round your answer to two decimal places if needed 1 Quiz 2 18 cm 3 cm 14 in 12 ft 24 cm 4 cm 50 m 9 217 9 21 8 12 1005 3 8A V 6 0 12 2412 74 6 in 30 m 8 cm 4 cm

Find the perimeter of polygon ABCDE A E 1 04 9 CON 8 7 6 5 4 32 1 10 9 8 7 6 5 4 3 2 1 1 2 3 34567890 4 5 6 8 9 1 0 D B 1 2 3 4 5 6 7 8 9 10 C X

Find the measure each shaded Central Angle A B 9 120

21 L 18 14 X 20 Q 12 R The polygons are similar Find the value of x

x E X 20 D 16 F 15 H 18 G 12 J The polygons are similar Find the value of x

c46 N 8 M Find the scale factor of the figures Then list all pairs of congruent angles AABC ALMN k B ZAZ ZB Write the ratios of the corresponding side lengths in a statement of proportionality

Given the circle below with secant YXW and tangent VW find the length of YX Round to the nearest tenth if necessary Y X 15 7 W

2 Find the solutions to the quadratic below using completing the square x 10x 4 0

Proving the First Case of the Inscribed Angle Theorem Given AB is the diameter of a circle and is one side of the angle that intercepts AC Prove mzABC is half the measure of AC 180 2x B You can draw line segment CD by the unique Since the triangle isl x D Triangle BCD is isosceles since BD and CD are both circle and all radii of a given circle are congruent EFO x A postulate of the its base angles are congruent

4 ERROR ANALYSIS Describe and correct the error in solving x 8x 10 by completing the square X x 8x 10 x 8x 16 10 x 4 10 x 4 10 x 4 V 10

2 Express the quadratic in vertex fo its vertex y x 12x 46

Express the quadratic in vertex form YOU DO ROUND 1 y x 16x 71

2 Solve for b in the triangle to the nearest hundredths A C 8m 25 B

ROUND 2 3 Determine the vertex of the quadr y x 6x 5

5 Which of the graphs below could be the graph of the quadratic y x 6x 3 Circle your answer Ay 4 2 Ay 4 3 2 5 XY 4 IA 6 3 2 Ay 4 2 2 2 1 x X YA Ex 4 6

Find the volume of each of the following Round your tenth if necessary 3 a square prism with base length 7 m and height 15 m 4 a cylinder with radius 9 in and height 10 in 5 a triangular prism with height 14 ft and a right triangle base with legs measuring 9 ft and 12 ft 6 a cylinder with diameter 24 cm and height 5 cm

Examine angles whose Prove theorems involving angles Apply involving inscribed angles G lie on a circle Apply theorems involving angles formed by a and tangent

side of the angle that intercepts AC Prove The measure of ZABC is half the measure of AC ZADC and ZBDC are supplementary since they form a The measure of ZADC 180 180 2x which simplifies to or twice the measure of angle ABC Since ZADC is a central that of AC FLL LLL LLLL 180 2x D B thlebblebi bla bla kbEWERBLETT Since the measure of ZABC is x the measure of AC is 2x pair The sum of their measures is 180 xo its measure 2x is equal to that C

Review Key Concepts The measure of an inscribed angle is half the measure of its intercepted arc Two inscribed angles that interceptthe are congruent An angle inscribed in a semicircle is a angle The opposite sides of a quadrilateral inscribed in acirde are supplementary If a tangent and chord intersect on a cirde the measure of each angle they form is the measure of its intercepted arc

The Angle Formed by a Tangent and Chord Theorem Angle formed by a tangent and chord theorem If a tangent to a circle and a chord intersect at a point c on the circle then the measure of each angle they form is one half the measure of its intercepted arc MZ mAB This also means that ZEAB is going to be equal to the measure of its intercepted arc BCA E A B LL F

The trinket store is open for 14 hours per day They sell an average of 5 trinkets per hour The back storeroom currently has 560 trinkets in it 1 Write an equation that estimates the number of trinkets T that will be in the storeroom after H hours 2 How many days will it take to run out of trinkets

Find the volume of each object 1 the rectangular prism part of the milk container 2 the cylinder part of the measuring cup 6 3 cm 7 cm 10 cm 7 cm 7 cm

The Third Corollary to the Inscribed Angle Theorem Third corollary to the inscribed angle theorem The opposite angles of a quadrilateral inscribed in a circle are supplementary A B up to C Remember that the measures of supplementary anglesadd O D This theorem means the angles B and D are going to be and angles A and be supplementary are going to Remember thata circle has 360 and that the measure of angle is half the measure of the intercepted

Using the Third Corollary to the Inscribed Angle Theorem The measure of 20 is x 2 and the measure of 2S is 9x 7 What are the measures of angles Q and S Since angles Q and S are opposite in a they are supplementary x 2 9x 7 180 10x5 180 Our 185 10 10 x 18 5 Plug this value of x into the expressions m20 18 5 2 180 20 5 0 0 of a quadrilateral inscribed T S m s 9 18 5 7 You could have also used the fact that opposite angles are supplementary to find the measure of angle S Q Not drawn to scale R

Inscribed angle theorem The measure of an inscribed angle is measure of its intercepted arc The Case 1 is one side of the angle Case 2 The center of the circle lies the angle The Case 3 the the circle lies within the angle of

Second corollary to the inscribed angle theorem An angle inscribed in a semicircle is a right angle Since DF is a diameter the angle is inscribed in half the circle or a Coroll ry to the Inscribed Angle Theorem This means that the inscribed angle is a angle A semicircle measures 180 so the measure of the angle would be half of that or E C LL

The First Corollary to the Inscribed Angle Theorem First corollary to the inscribed angle theorem Two inscribed angles that intercept the same arc are congruent ZKJL and ZKML are their angles intercept the same arc KL same A JM because We can also say that JKM and congruent because their angles also intersect the are J K M

Central Angles The measure of a central angle is equal to the measure of its intercepted arc C 42 A B

An inscribed angle is an angle whose sides are chords is on a circle and whose An intercepted arc is the arc that lies in the interior of an and has endpoints on the angle C B angle

Find the area of polygon JKLMNO K 104 886 9 7 bl 2 10 9 8 7 6 5 4 3 2 11 123 2 456 M 1 2 3 4 5 6 7 8 9 10 N

Angle ABD measures 4x 10 Angle ACD measures 5x 2 A D E C B What is the measure of arc AD O 12 O 58 O 96 O 116

Angle BAC measures 56 D B O What is the measure of angle BDC O 28 O 34 O 56 O 112

In circle V angle WXZ measures 30 Line segments WV XV ZV and YV are radii of circle V W U X Y What is the measure of WUX in circle V O 60 O 90 O 120 O 150

104 D 79 G LL F What is the measure of arc ECF in circle G O 52 O 98 O 158 O 177

Line segment GJ is a diameter of circle L Angle K measures 4x 6 H K What is the value of x O 21 24 O 32 044

Line segment XY is tangent to circle Z at point U X T U W Y 12 If the measure of UV is 84 what is the measure of ZYUV A O O O O 42 84 96 168

In circle D angle ADC measures 7x 2 Arc AC measures 8x 8 A B C What is the measure of ZABE O 36 O 43 O 72 O 144

10 Scott set up a volleyball net in his backyard One of the poles which forms a right angle with the ground is 7 feet high To secure the pole he attached two ropes from the top of the pole to a stake 4 feet from the bottom of the pole Find the total length of the two ropes A 160 ft B 8 5 ft C 4 ft D 8 3 ft 10

K 70 116 1 What are the measures of JK and ZKIJ Measure of JK Measure of ZKIJ

88 D U 111 A What is the measure of A O 44 O 50 O 64 O 92

40 Q R PR and gs are diameters of circle T What is the measure of SR 50 80 100 120

Justifying the Second Corollary to the Inscribed Angle Theore Explain how you can use the inscribed angle theorem to justify its second corollary that an angle inscribed in a semicircle is a right angle