2D Geometry Questions and Answers

of point line and distance along a line line lowing terms precisely in terms segment angle and perpendicular lines P 3x 5 Lesson 1 2 Checkpoint Once you have completed the above problems and checked your solutions complete the Lesson below Complete the Lesson Reflection above by circling your current understanding of the Learning Goal 1 OS bisects PQR What is mzPQR Hint Solve for x and plug the value back in Don t forget to add the final two angles together 2 25 Starting S Getting there R Got it We in

10 MA bisects segment CB at midpoint M Based on the definition of angle bisector and midpoint find the value of x and the following measures MB CM CB O 0 B

HW 1 Which of the following is NOT a property of perpendicular lines A They intersect at one point B They intersect to form a Right Angle C The intersection can form 90 angles OD They intersect to form acute angles A 4 Which of the following is NOT properly named based on the figure below 4 C Complete problems 1 10 for independent practice When you are finished check the solutions with your teacher B A ray CA B LACB C ray AB OD ZBCA 3 Which of the following is NOT a type of bisector A Dimensional Bisector B Segment Bisector C Perpendicular Bisector D Angle bisector 5 Which of the following best classifies the angle measurement of ZLMN 0000 L M N A Acute Angle B Right Angle C Obtuse Angle D Straight Angle R

MP bisects segment LN at midpoint M Based on the definition of angle bisector and midpoint find the measures of m 1 segment LM and MN m21 LM MN 1 M LN 30

EXPLAIN 3A Constructing an Angle Bisector Read Explain 3A and complete Your Turn 1 2 adapted from Lesson 1 2 An angle bisector is a ray that divides an angle into two angles that both have the same measure In the figure BD bisects LABC so m ABD m CBD The arcs in the figure show equal angle measures Example 1 BD bisects LABC What is m ABC Information Solve Ego mzDBC mzABD 65 mzABC mLABD mzDBC m ABC 65 65 mzABC 130 8 Determine the value of x 26 5x 11 26 5x 11 Definition of an angle bisector 15 5x Subtract 11 on both sides Divide by 5 on both sides 3 x Your Turn If m FCD x 48 mzBCF x 17 and m BCD 95 then find the value of x B C F D

Determine if the angle pairs are complementary supplementary or neither given m PRO 99 mzPRQ 81 mzPRS 9 and m2ORS 90 1 ZPRQ and ZPRO are 2 LORS and LPRS are 3 20RS and LSRQ are 4 ZPRQ and LPRS are ST P R

Name 22 in many different ways as possible 22 8 M 3 2 E D Without seeing a figure give another name for ZMKG

HW 1 Which of the following is the correct way to name a line segment A AB B CD OCEF OD DC plete problems 1 10 for independent practice When you are finished check the solutions with your teacher 3 All points between and including endpoints describes which of the following terms A angle OB line OC line segment Dray 5 Which of the following is the midpoint formula A a b c B 1 2 X C x y z OD 221 22 21 2 What does the symbol QR represent A line segment QR OB angle QR C ray QR OD line QR 4 If BD is bisected by point C then BC CD BD 0000 A Segment Addition Postulate B Definition of a Midpoint C Addition Property of Equality D Definition of an Angle Bisector 6 Which of the following is the distance formula A x x y y B x y x y C x y x y D x x y y

7 e kolu olan bir merdiven bir ucu duvar zerine gelecek bi imde zemin zerinde konumland nda olu an a l leri ekilde veriliyor Duvar Zemin 55 A 80 B B 85 X E 65 A E ve B do rusal oldu una g re m AEA x ka derecedir C 90 A B D 95 E 100 6 A 7 B

Determine the value of x for which r s Then find m21 and m22 m 1 30 6x m2 40 26x The value of x for which r II s is Type an integer or a decimal m21 Type an integer or a decimal m22 Type an integer or a decimal S 2

Use the graphs of f and r to describe the transformation from the graph of f to the graph of r f x 3r 5 The graph of r is a of the graph of flby a factor of

How many significant figures should be recorded for the answer to the multiplication problem below 24 32 x 0 010 significant figures

4 J I K A reflection across x 1 B reflection across y 2 C reflection across the y axis D reflection across x 2 x

The graph of f x is shown below Find the graph of f x N 10 4 20 2 1 5 1 2 3 4 5 6

If JM 5x 8 and LM 2x 6 which expression represents JL J O 3x 2 O 3x 14 07x 2 O 7x 14 K M

Use suitable labelled line diagrams to show how the following tools are used to check the squareness of a simple rectagular building Builder s square

A DA C120 6 m B B

If TU p 4 and SV p 44 what is the value of p W T S HH V

XZ is a midsegment of AVWY If VW p and XZ p 25 what is the value of p Y V N X W

We ve seen that as the sailboat logo is resized by dilation the line segments that make up the logo may be mapped onto parallel lines or stay on the same line The lengths of the image are the lengths of the preimage multiplied by the scale factor Now we will use GeoGebra to compare the angles of a dilated figure to the angles of the original figure Open dilations again Then complete each step below For help watch this video to learn more about measurement tools in GeoGebra Part A Measure and record the measures of these angles in the original logo Then set n 0 5 and n 2 and record the measures of the corresponding angles in each resulting image BIX X 12pt AEVO Angle Original Measure Measure After Dilation n 0 5 FGB 2GBC ZLKJ n 2 cluder formarring 1154 15000

Select the correct answer from each drop down menu reflection 18 16 14 12 10 0 8 6 2 6 R 8 10 12 E F G 14 16 18 PQRS and EFGH are polygons that can be mapped onto each other using similarity transformations The transformation that maps poly PQRS onto polygon EFGH is a rotation followed by dilation with a scale factor of 2 v

Reflectional Symmetry Do the flags below have reflectional symmetry If so draw the appropriate lines of symmetry across each flag Consider how both the shape of the flag the design on the flag would affect this concept 10 stil te

List 3 different objects that you encounter every day with reflectional symmetry List 3 different objects that you encounter every day with rotational symmetry

Do the items below have rotational symmetry If so by how many compl degrees What s your mathematical reasoning Japan Systemunye 1sbiene0 Ston galt eri od erii peit

Model a real life staircase using function 18 18 a pi

Simplify the trigonometric expression cos x sec x tan x

Simplify the trigonometric expression 6 sin x sec x tan x

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

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

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

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

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

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

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

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

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

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