Geometry Questions

Lesson 21 Practice Problems 1 The triangles here are each obtained by applying rigid motion 5 10 N 11 3 12 8 4 2 The quadrilateral is a parallelogram Find the measure of angles 1 2 and 3 13 9 5 14 10 80 6 15 a Which triangles are translations of triangle 17 Explain how you know 11 b Which triangles are not translations of triangle 1 Explain how you know 7

Cool Down Mystery Quad Quadrilateral ABCD has both reflection and rotation symmetry What type of quadrilateral could ABCD be Show or explain your reasoning

4 Do the shapes below have rotational symmetry Why or why not If so by how many degrees

D Name the transformation that maps the blue pickup truck preimage onto the red pickup image

2 Are the transformations below rigid or non rigid Explain each of your answers in detail o 2

3 How many lines of symmetry exist in each of the flowers below Draw them please

X PY H W BALD Transformations mation given Graph the image of the figure using the transformation given 1 translation 2 units left and 7 units up X nosalamati Name Seda aliny Stmonlean 2 dilation of 2 5 F hodnotbal songs lemey Batkitar T Include Vector Rules X Rule M 2 5x2 5y

23 rotation 90 clockwise about the origin D P X 24 rotation 180 about the origin Z H Y x

se a graphing utility to approximate the local maximum value and local minimum value of the function f x 0 4x 0 6x 3x 4 for 6 x 4 sing a graphing utility graph the function for 6 x 4 and 25 y 10 Choose the correct graph below A Z Q N O B O C F

3 rotation 180 about the origin R Ay B K Z Rule 4 reflection across the y axis ainu noitalansuj S M H F y Rule 2

PRACTICE ANOT Of the infinitely many lines that are tangent to the curve y 8 sin x and pass through the origin there is one that has the largest slope Use Newton s method to find the slope of that line correct to six decimal places

ct the figure as indicated Label the image using prime notation audi ladnd besthet reflection across the x axis tooleretuo 200 poiro 14 reflection across the x axis 10 migno F X Z AX

Rotate the figure as indicated Label the image using prime notation digit 19 rotation 180 about the origin nouselts 20 rotation 90 counterclockwise about the co origin Z H N A D Ay W G

5 W Wy F F Rule x A R R A N N Rule

awise noiloaftur 21 rotation 90 counterclockwise about the origin B N E X 22 rotation 180 about the origin H T y X

17 reflection across the y axis M W N X 18 reflection across the y axis P g

9 translation 5 units left and 2 units up M X 10 translation 2 units right and 5 units down B y Z S X

12 translation 4 units right and 1 unit up Ay A 7 N X

Lesson Cool Down Triangle Angle Sum a Third Way Elena wants to prove that the measures of the 3 angles in a triangle always sum to 180 degrees She starts by using rigid motions to rotate triangle ABC 180 degrees around 2 midpoints 9 c C D B bo B Explain how Elena labeled her diagram and finish her proof MLA m B mcc 180 bo A g C C E

15 reflection across the y axis D P AX 16 reflection across the x axis Toda 081 aolimot Y W y Tapiolandiuto ne X

11 translation 2 units right and 2 units up M U y X 12 translation 4 units right and 1 unit up y A N 1x X

its 7 The 3 circles in the diagram have centers A B and C D B a Explain why segments AB and AC have the same length b Classify triangle ABC Justify your classification c Mai wants to construct a regular hexagon inscribed in the circle centered at C Will these instructions work to finish the hexagon from the construction given If so explain why Mai is correct If not finish the construction correctly i Draw the circle centered at D with radius CD ii Mark the intersection of the circle with the circle centered at C and label that point E iii Draw the circle centered at E with radius DE iv Mark the intersection of the circle with the circle centered at D and labe that point F v Connect ABCDEF to make a regular hexagon

In each question lines AI and GJ are parallel and intersected by the transversal line FE 1 Angles EBI and BCD are corresponding angles Use a transformation that takes angle EBIto angle BCJ to prove that corresponding angles are congruent 1 G C F A 2 Angles ABC and BCJ are alternate interior angles Use a transformation that takes angle ABC to angle BCJ to prove that alternate interior angles are congruent Label any other points on the figure that will help to define a transformation E G B C E B

24 3 Priya followed this set of instructions to make quadrilateral ACBD Choose a description you can be sure is accurate for the shape she constructed 20 2 2p a Draw 2 points A and B b Draw a circle centered at A with radius A B c Draw a circle centered at B with radius AB d Label the intersection points of the circles C and D Draw segments AC BC AD and BD A 2 congruent sides but not all 4 B 4 congruent angles C 4 congruent sides D 4 congruent sides and 4 congruent angles 4 What is the definition of a circle Figura geom trica delimitada por una circu curva cerrada cuyos puntos equidistan a 5 Triangle ABC is isosceles Use straightedge and compass tools to construct the perpendicular bisector fo segment AB r B

21 96 87 125

4 25 40

Brianna is taking part in a lottery for a room in one of two new dormitories at her college She will draw a card randomly to determine which room she will have Each card has the name of a dormitory X avier or Y oung and also a two person room number or an apartment number Forty percent of the available spaces are in X Seventy percent of the available spaces in X are rooms and 20 of the spaces in Y are rooms If Brianna gets an apartment what is the probability that she is in dorm Y The probability is Tyne an integer or decimal rounded to three decimal places as needed CIES P Room X 0 7 0 4 P Y 0 6 Room 0 28 0 3 Apartment 0 12 02 Room 0 12 P Apartment Y 0 8 Apartment 0 48

TS shows an undirected weighted graph Rajah di bawah menunjukkan satu graf tak terarah dan berpemberat D 2 6 7 3 H E G 00 8 9 13 G 10 B 4p 25 The minimum total weight of the tree for the graph is 4p q The maximum total weigh tree for the graph is 4p q 2 Calculate the values of p and q Jumlah nilai pemberat minimum pokok bagi graf itu ialah 4p q Jumlah nilai pemberat mak pokok bagi graf itu ialah 4p q 2 Hitung nilai p dan nilai q 5 marks 5 ml chows 11 states except Federal Territory of Kuala 400 13

39 Sey eller Hint Okyanusu ndaki 115 ten fazla ada zerinde kurulu bir lkedir Sey eller bayra yapmak i in a a daki dikd rtgenin k sa ve uzun kenarlar n n zerine e it aral klarla iki er nokta i aretleniyor Bu noktalar dikd rtgeni 5 alana b lecek bi imde A k esiyle birle tiriliyor ve a a daki gibi boyan yor E A 15 C C 6 3 37 AB 3 37 birim AC 15 birim oldu una g re CE ka birimdir A 2 B 4 B D 6 5 E 9

Geometry For 25 28 tell whether the figure can be folded in half so that one side matches the other Yes No 28 27 26 25 S D

Write short answers Consider the inverse tangent function defined by y tan xory arctan x Complete parts a d a What is its domain Type your answer in interval notation Simplify your answer Type an exact answer using x as needed Use integers or fractions for any numbers in the expression b What is its range 00 00 Type your answer in interval notation Simplify your answer Type on exact answer using as needed Use integers or fractions for any numbers in the expression c Is this function increasing or decreasing O decreasing O increasing d is there any real number x for which arctan x is not defined If so what is it or what are they O Yes o bo Use a comma to separate answers as needed

Lesson 2 Practice Problems 1 Line SD is a line of symmetry for figure is congruent to HMZDS because sides AX and HM are corresponding a Why is Noah s congruence statement incorrect b Write a correct congruence statement for the pentagons X 2 Figure MBJKGH is the image of figure AFEKJB after being rotated 90 degrees counterclockwise about point K Draw a segment in figure AFEKJB to create a quadrilateral Draw the image of the segment when rotated 90 degrees counterclockwise about point K Write a congruence statement for the quadrilateral you created in figure AFEKJB and the image of the quadrilateral in figure M BJKGH A D B M E K

Given csc 2 Find all trigonometric function values for 8 with 8 in quadrant II Round all non termination decimals to three places sin a cos a tan a cut a sec a cac a

Macmillan Learning The mil is a type of angle measure used in the military This term is derived from milliradian and 1000 mils equal 1 radian What is the degree measure of 1 mil Use decimal notation Give your answer to three decimal places Include the degree symbol in the answer 1 mil A target is 1 yard wide and subtends an angle of 1 mil in a soldier s field of vision How far from the soldier is the target Suggestion Think of the target as an arc of a circle yards between the soldier and the target How many mils are there in a circle Use decimal notation Give your answer two decimal places

O Macmillan Learning Convert an angle of radian measure 6 to degree measure Give an exact answer Include the degree symbol in answer 67 radians

A right triangle has legs of length 4 and 16 Use the Pythagorean theorem to find the length of the hypotenuse Express numbers in exact form Use symbolic notation and fractions where needed length of hypotenuse

Macmillan Learning Recall that in a triangle the angle sum is r radians or 180 An equilateral triangle has all three angles equal What is the degree measure of an angle of an equilateral triangle Give an exact answer Use symbolic notation and fractions where needed Include the degree symbol in your answer angle

x 3 In the graph below drag the green x intercept s to the correct position s Drag the red vertical asymptote s to the correct position s Drag the two orange points to form the correct slant asymptote Determine several points of the function and drag the blue point to one of these locations Choose a point that is not an x intercept and for which the y coordinate is a multiple of 0 1 Otherwise you won t be able to drag the blue poir to the exact location When finished click CHECK 10 6 2 5 10 5 I 10

The graph of f x 2 13x 54x 72 is given below Use the graph of f to solve the following equation r 13x 54x 72 0 10 9 8 7 6 5 4 3 2 1 1 2 3 4 5 8 9 2 3 7 8

Determine the perimeter of given figure on th coordinate plane Round your answer to the nearest hundredth if necessary Figure ABCDEF A YA F 86 4 2 B 8 0 O 8 6 4 22 LE 6 8 C 2 4 6 8 D AX

Prob 1 3 General Addition Rule Set backpound Clear fame Complete each probability model by finding the probability of B only Warm up Shade the region that represents the union on the two events A or B Then momote tha nenhahility A 0 25 B A 0 05 B

Show how each vertex of AEFG maps to its image Describe in words how to map AEFG to its image AE F G using a reflection 6 V G 4 R A fu Ay 10 8 6 4 2 2 4 6 101 Complete the table with the coordinates of the image points E F and G AEFG 4 5 2 5 3 2 E F G Type ordered pairs E F G AE F G

Given AXYZ ARST find the values of a and b N 5b 3 70 4a 4 R 62 T 48

3 4 Angles 4 5 and 6 are in the ratio 2 5 3 Find the measure of each angle 4 5 Find m 1 1 6 x 8 2x

Y 2 Z 16 reflection across the x axis P y W y 18 reflection across the y axis Ay 10 X Boisinuos D doijet X X

20 rotation 900 origin D siter H 22 rotation 180 about the origin B Ay W T G y X H X 24 rotation 180 about the origin X orli 32010 OTSE

B A F S N H 10 translation 2 units right and 5 units down Y Z X S P 12 translation 4 units right and 1 unit up Atel X rli joods 081 XY

2 dilation of 2 5 6 4 reflection across the y axis R J F A H F R W y N X X

10 5 TT VE 10 0 5 is 5 X 10 A triangle on the coordinate plane has points located at A 1 6 B 4 3 and C 1 1 What is the area of the triangle I Submit of 9

2 G GSR 5 2 The accompanying diagram shows two similar triangles A C dant X Which proportion could be used to solve for x 32 12 x 9 15 x 24 32 15 12 x 32 B D 24 9 9 24 15 15 X 12 15