2D Geometry Questions and Answers

n Your Turn Use the Triangle Inequality Theorem to tell whether a triangle can have the following sides with the given lengths Explain 1 12 units 4 units 17 units EXPLAIN 3 largest angle Read Explain 3 and complete Your Turn 1 2 adapted from Lesson 7 3 Show all your work In relation to each other the relative size of the side lengths of a triangle can be used to determine the relative size of the angles This means that if you are given the side lengths in order you can use them to order the angle by size largest side Ordering a Triangle s Angle Measures Given Its Side Lengths Side Angle Relationships in Triangles 2 24 cm 8 cm 30 cm Embr medium side medium angle In any triangle the larger angle is opposite the longer side AB AC BC SO mzC m2B mzA B Example For each triangle order its angle measures from least to greatest In the figure we see that the sides from shortest to longest are AB BC and AC The angles opposite these sides are LC LA and LB respectively So the order of angles from least to greatest is LC LA and LB shortest angle shortest side 2 4 15 3 A C 12

Learning Goal I can prove the following theorems about triangles The segment joining midpoints of two sides of a triangle is parallel to the third side and half the length X Q Lesson 8 4 Checkpoint Once you have completed the above problems and checked your solutions complete the Lesson Che below Complete the Lesson Reflection above by circling your current understanding of the Learning Goal 1 Given the figure below solve for x Then find the value of QP H x 3 x 3 3x 3 P 2 Given the figure below solve for x Then find the value of XV x 2 I V G P Starting Getting there

m Theorem Operty of Equality ty of Equality ms mzMJK 3x 16 D 7x F H E Lesson 8 NOREER O

Cool Down Make Your Own Invent measurements that would show triangle XYZ is similar to triangle NLM using the Side Angle Side Triangle Similarity Theorem Z N M

angle DBC angle ABE angle ABC A In the diagram which angles are vertical angles Choose 2 pairs angle EBD E B C angle DBC O O O O angle ABE O O O angle ABC O OOO angle EBD O O O

In the triangle below x 8 Use the Law of Cosines to solve the triangle Round your answers to two decimal places A B 12 cm O B 0 O 18 cm x cm C

tan2x sec2x 9 Its only giving me one value when there is multiple in the solution set

10 Suppose that you decide to buy a car for 36 635 You saved 9000 for dow payment and you can get a 5 year car loan at 7 88 Use the formula PMT P 5 8 pts 1 1 nt

M Prove AOLN AMLN N bisects ZOLM LN bisects ZONM L O Statement Reason

14 Given ZP ZR PQ II SR Prove PQRS P Statement Reason

In I Identify the following angle pairs as Corresponding Angles Alternate Interior Angles Same Side Interior Angles Vertical Angles or Linear Pairs a 41 and 27 c 43 and 26 b 22 and 4 d 45 and 48 m 4 3 1 2 76 b

d A a C Y AB BC

B3 Find BD 8 6 D 12 X B

B6 Solve for RQ R 10 48 T 3

Solve for x 21 15 35

ve for x B x 3 9 4 A 6 C

Solve for x B 35 15 21 XU x 1 C

Find mzSQR if m 2 13 S P 2 Q

A3 Find BD 9 9x1 6 12x 16 144 12x 12 12 12 X 12 9 A D 16 B

Find xif m22 1 28x and m2XVW 59x 1 V 2 1 W P

Find xif m22 4x 5 and m21 5x 2 Y X Z

B D 2 A 2x 2 5 C

Esperanza is the owner of an independent motel that has 40 rooms She finds that if she charges 30 per night all the rooms will be rented Thereafter for every 4 she raises the room rate 3 fewer rooms will be rented out 2 12 Write a function equation for the number of rooms rented as a function of the price of a room 5 13 Write an equation describing the income for the motel for one night as a function of the price of a room

A1 m SUT 34 Find m21 S P 2 T

Question 10 Triangle KLM is formed by connecting the midpoints of the side of triangle HIJ The lengths of the sides of triangle HIJ are shown Find the perimeter of triangle KLM Figures not necessarily drawn to scale M Watch Video K 10 Show Examples

Identify all pairs of angles of the given type 1 8 2 3 a consecutive interior b alternate exterior Exercise 3 c corresponding d alternate interior 76 45 Classify the pair of numbered angles in the figures below as one of the following corresponding alternate exterior or alternate interior X 4 5 5 4

The given line markings show how the roads in a town are related to each other J N 49 F LA M K GH HUM a Name a pair of parallel lines L c Is ray GN 1 line JL Explain 62 b Name a pair of perpendicular lines

1 Think of each segment in the figure as part of a line Which line s or plane s appear to fit the description A E F D H C G a line s parallel to line GH and containing point F b line s skew to line GH and containing point F c line s perpendicular to line GH and containing point F d plane s parallel to plane GHD and containing point F

AABC is the pre image f the length of AB is 31 and the length of XZ is 25 what is the scale factor round to the nearest ten place A C N B

Use your classwork to fill in the blanks for all the properties of kites All kites have pair s of congruent sides to each other The diagonals of all kites are All kites have at least one diagonal that is All kites have at least one diagonal that bisects the angles at its All kites have at least pair s of congruent angles

2 Draw in the diagonals of the kite below and use the properties of a kite to mark congruent segments congruent angles and perpendicular segments CW LCW HW

32 T 24 B V 19 W 21 S 1 RS 3 WS 5 TW 38 2 TQ 4 QV 6 WV

8 Find AP 11x 14 E C

Find the unknown angle measures m P 0 Q N 138

Actual lengths of pregnancy terms for a particular species of mammal are nearly normally distributed about a mean pregnancy length with a standard deviation of 10 days About what percentage births would be expected to occur more than 30 days after the mean pregnancy length About of births would be expected to occur more than 30 days after the mean pregnancy length Type an integer or a decimal

In circle O the length of PQ and m POQ 120 Find the area shaded below Express your answer as a fraction times 7 P

14 Given the points A 2 1 3 and B 4 1 3 determine the coordinates of the point on the x axis that is equidistant from these two points

21 sin 150 22 tan 945

0 A 67 Round to the nearest degree as needed A C b 11 32 m Do not round until the final answer Then round to the nearest hundredth as needed C 15 21 m Do not round until the final answer Then round to the nearest hundredth as needed 44 B

ger ek say larda tan ml do rusal aksiyon ve F 2x 1 f 3x 15x 5 du una g re f 10 de erini bulunuz

In the figure a line segment of length L is to be drawn from the given point to the positive x axis in order to form a triangle For what value s of L can the following be drawn a two triangles b exactly one triangle c no triangle a For what value s of L can two triangles be drawn Select all that apply AL 4 A L 5 B L 4 BILB AL 5 b For what value s of L can exactly one triangle be drawn Select all that apply B4 L 5 C L 5 L 5 c For what value s of L can no triangle be drawn Select all that apply B L 4 D 4 L 5 C L 5 DL 4 XD 4 L 5 3 4 EL 5 DE L 4 EL 4 Similar question

Watch the video that describes Using to solve a triangle SAA Click here to watch the video Find the exact length of side a Do not use a calculator 159 Length of a 1 120 B B 3 Simplify your answer Type an exact answer using radicals as needed Rationalize all denominators

18 tan 945

1 Let m x x e Find functions f x and g x so that m x f g x and neither f x g x x x nor

3 Determine whether each pair of angles is co terminal or not a 23 383 e 19 390 b 41 421 f 410 3190 4 Calculate the next two positive co terminal angles a 132 b 275 5 Calculate the next two negative coterminal angles c 50 310 g 280 2320 d 38 398 k 105 465 c 305 100

Find the indicated arcs and angle measures B A mCS mAS m ABS m SBC O O 58 C S

TT VE X Using the sketch pad trace the vertical asymptotes in green Give the equation of each vertical asymptote and give the corresponding factor that will appear in the rational function smaller vertical asymptote odd or even power factor larger vertical asymptote odd or even power factor Should these factors vertical asymptotes appear in the numerator or denominator of the function

On a baseball diamond a square the bases are 90 ft apart T S ft P H 90 Use the Law of Sines to find the distance from home plate to second base in feet Round your answer to one d place

Determine if triangle FGH and triangle IJK are or are not similar and if they are state how you know drawn to scale Answer Attempt 1 out of 2 F G 100 135 4 75

Question Find the value of a to the nearest tenth X 6 8 5