High School Geometry Questions

APS ST

45 6

6 10 in Y 133 17 in Z

20 279 Round answers to nearest whole number

R S 45 cm 22 45 cm T

45 6

D 6 5 cm 85 F 11 2 cm E 4 F E 19 4 mm 71 D 15 2 mm

20 X 13 on to the given blank paper 2 Round answers to nearest whole number X 39

21 49

20 fi 15 A 36 116 S T ZR Area

10 Given AABC has the following coordinates A 0 5 B 2 1 C 2 3 Perform the following transformations 1 Translate AABC along the vector 5 7 A B 2 Dilate AA B C by a scale factor of k from a Center of Dilation of 3 2 B A C C

B 10 7 D C 8 19 E 13 F I Lin knows that angle A is congruent to angle D She claims that triangles ABC and D must be similar Convince Lin that the triangles are not similar

Your Turn Find the unknown arc measure 1 mKLN M 48 K Q 86 79 N

Your Turn Find the measures using the figure provided 1 mPN 2 m2MNP 61 N 238 M

An equilateral triangle is inscribed in a circle Use your knowledge of equilateral triangles to strengthen your understanding of inscribed angles and their arcs You may describe or demonstrate your knowledge of the Inscribed Angle Theorem with an equilateral triangle inscribed in a circle Optional Complete problems 1 5 13 21 24 from your textbook on separate lined paper for extra practice When you are finished check the odd problems for solutions at the back of the textbook

The circumference of a tree is Use 3 14 for m 2 The circumference of a circular fountain is 32 feet What is its diameter Round to the nearest tenth of a foot Use 3 14 for m

It costs 7 cents per square inch of pizza Your Turn 1 A circular swimming pool has a diameter of 20 feet To the nearest square foot what is the smallest amour material needed to cover the area of the surface of the pool Use 3 14 for

The center of the circle is C Find each measure using the appropriate theorems and postulates 1 m MLP 70 M 60 CN Elaborate 2 Select which statements are true or false in this figure using the theorems you learned in this lesson There are three true statements

5 A blimp that is filming a football game makes a 7 angle of depression to the stadium If the blimp s altitude is 400 m find the line of sight distance from the blimp to the stadium

The world s tallest flagpole is 282 ft tall The shortest shadow cast by the pole is 137 ft long Find the angle of elevation from the tip of the shadow to the top of the flagpole

In 11 13 Draw a picture for each problem then solve 11 A person standing 30 feet from a water tower can see the top of the tower at a 55 angle of elevation person s eye level is 5 feet from the ground Find the height of the water tower

A surveyor is looking up at the top of a building that is 140 meters tall His eye level is 1 4 mete angle from his eyes to the top of the building above the ground and he is standing 190 meters from the building Calculate the measure of the 140 m 8 A hot 190 m ta XI 1 4 m

3 Find the arc length of BC O B B 56 4 Find the measure of ZD felong C 50 C 134 OP WAS HAZME

8 A hot air balloon lifts 125 feet into the air The diagram below shows that the hot air balloon was blown to the side How long is the piece of rope that connects the balloon to the ground 9 x 1 4 m 125 ft

A boat is sailing about 400 ft from the cliff at the shore of a lake A sailor on the boat uses a device to measure the angle of elevation between the lake level and the top of the cliff Find the height of the clif 15 Cliff h

or is looking up at the top of a building that is 140 meters tall His eye level is 1 4 meters above the ground and he is standing 190 meters from the building Calculate the measure of the angle from his eyes to the top of the building 140 m 190 m ta 1 4 m www

H 5 ve for x and y N 2y 6x 9 3y 4x 11 F G om your textbook on separate lined paper for

10 Use the diagram to the right to find the total height of the flagpole 5 5 ft 23 30 ft Will

Lesson 15 2 Checkpoint Once you have completed the above problems and checked your solutions complete the Lesson Checkpoint below Complete the Lesson Reflection above by circling your current understanding of the Learning Goal 1 Find the following angle measures of the inscribed quadrilateral mzRQP mzPSR m SRQ m2QPS 5x 20 10x R 7x 8

Find mcDAB DAB DEB mzDAB 63 3 Find mX2 108 18 126 43 mDE mEB Arc Addition Postulate For 2 3 use Circle C 2 Find mWX Inscribed Angle Theorem Your Turn Use the Inscribed Angle Theorem to find missing angle measures 1 Find the arc measure of CE Substitution Simplify X W Y SA C 9 106 Z

1 m MPK 2 MPE 61 M 127 D O 134 111

Your Turn Determine the unknown values in each figure 1 117 h 2 4 m CDA 45 Elaborate Problems 3 6 requires you to apply your knowledge from Lessons 15 1 through 15 3 Refer to the figure for Problems 3 6 AB is tangent to OC at point B and AD is tangent to OC at point D Determine the angle measures 3 m BCD 5 m BED 6 m DBA N 5 32 B

1 Reflect Both lines in the figure are tangent to the circle and AB is a diameter What can you conclude about the tangent lines

HW Complete problems 1 7 for independent practice Find the measure of the arc or central angle for the following circles 1 Find the measure of ZRQS R S D Use the Inscribed Angle Theorem to find missing angle measures 2 Find the measure of ZD 124 3 Find the arc length of BC 4 Find the measure of LD When you are finished check the solutions with your teach 134

Lesson 15 4 Checkpoint Once you have completed the above problems and checked your solutions complete the Le below Complete the Lesson Reflection above by circling your current understanding of the Learni 1 Find the value of x and J M 6 X N L H K 10 2 Find the value of y and the length of each secant segment y 18 7 N J 10 M 9 L

HW Complete problems 1 4 below for independent practice When you are finished check the solutions with your teacher For 1 and 2 use the figure on the right LK and LM are tangent to the circle Both KJ and MJ connect to the center of the circle at point J K 1 What is the measurement of ZKJM 2 What is the measurement of ZLMJ 60 4 What is the measurement of LADC and LABC L For 3 and 4 use the figure on the right CB and CD are tangent to the circle Both BA and DA connect to the center of the circle at point A 3 What is the measurement of BCD M B 127 G Optional Complete problems 4 8 13 16 18 19 from your textbook on separate lined paper for extra practice

1 Find the value of x Round the answer to the nearest tenth or leave it in radical form 6 O B 4 X C 2 On a bird watching trip you travel along a path tangent to a circular pond to lookout station that faces a hawk s nest Given the measurements in the diagram on your bird watching map how far is the nest from the lookout station Nest X 25yd Lookout Station 100yd Path

Lesson 15 3 Checkpoint Once you have completed the above problems and checked your solutions complete the Less Checkpoint below Complete the Lesson Reflection above by circling your current understanding of the Learning Use the figure below for 1 and 2 T R S 42 P 1 PR is tangent to circle Q at R and PS is tangent to circle Q at S Find mZRQS 2 Use your knowledge of central and inscribed angles to find m RTS

Critiquing Your Friend s Work Your friend was asked to solve for the value of y using secant secant product theorem but solved for it incorrectly Help your friend by explaining or demonstrating how to solve for y correctly 2 Solve for y Your Friend s Work HL JL NL ML y 10 27 9 10y 243 y 24 3 y 24 3 Your Work N H y 18 J 10 M 9

Your Turn Find the measure of the arc for the following circles 1 Find the measure of RS OF O 2 Find mBD If mEF 45 and mZACD 56 determine mBD using the appropriate theorems and postulates AE BF and DC intersect at Point C 3 Find the value of x 4x 21 VAW 78

Try This For the given image name the 2 tangent lines and the points of tangency For the given image name the 2 tangent lines and the 3 points of tangency Tangent lines Points of tangency EXPLAIN 1 Proving the Tangent Radius Theorem Read the section below and complete the following activity adapted from Lesson 15 3 Tangent Radius Theorem If a line is tangent to a circle then it is perpendicular to a radius drawn to the point of tangency C

Checkpoint Once you have completed the above problems and checked your solutions complete t below Complete the Lesson Reflection above by circling your current understanding of the L 1 Find the value of x given m2SAR 7x 7 and mzSQR 9x 7 e 9x 17 7x 7 R S 9x 7 2 Find the value of x Then find the measure of RQ mRP 9x 17 mfQ 6x 1Z meRPQ 5x 15 Given Sr 15 R 6x 12

Guided Exanie 4 Name three points on the line y 2 4x

156 Slope run Reminder The slope of a line is how steep it is It is calculated as the ratio of Start at the bottom left corner of the graph paper and make a staircase with the indicated rise anc run Then draw a line touching the tips of each stair A rise 1 run 1 slope of 1 C rise 2 run 1 slope of 2 B rise 3 run 2 3 slope of 2 D rise 1 run 2 slope of

5 An airplane is flying 31 yards above the ocean Find the angle of depression from the plane to the boat when the plane is a horizontal distance of 50 yards from the boat X 31 yd

Find the missing measure round to the nearest tenth 3 At a point 250 ft from a building the angle of elevation from the ground is 25 Find the height of the building x X 250 ft 25 d or sobie fion

In 1 2 label each angle as an elevation or a depression 1 a Ll b 42 C 23 d 24 Refit 3 2 2 a Zl b 22 C 23 d 24

4 The horizontal distance from a person to a kite is 85 ft and 100 ft of string has been let out Use the diagram below to find the angle of elevation from the person to the kite 100 ft 85 ft

Flat Tax Some Americans are supporting switching to a flat income tax rate of 15 How much would you pay under this plan Your Income X 15 or 15 Calculator Tip To multiply by a percentage you can use your calculator in two ways You can use the percent symbol key or you can enter the percentage as a decimal To change a percentage to a decimal move the decimal point two digit places to the left Example 20 becomes 0 20 Regressive Tax Plan Mark X next to the row that matches your yearly income TOTAL Proposed Regressive Plan 40 on income up to 25 000 30 on income between 25 000 and 34 000 25 on income between 34 000 and 44 000 20 on income between 44 000 and 80 000 10 on taxable income over 80 000 Calculate your tax For example 10 000x40 4 000 in tax

Find the slope of the line through each pair of points X X X Y 3 2 10 8 16 1 26 X X X ya 4 17 5 15 13 13 5 15 17 1