Solution of triangles Questions and Answers

Which of the following can be used when two triangles share an angle Substitution Reflexive Alternate Interior Angles Vertical Angles

Use circle J 5x 15 K 120 L J What is the value of x

4 Find m A C 8 cm B 105 32 cm 14 A

1 Given the two functions f x x 4x 1 and g t 1 t a Find and simplify f g 4 b Find and simplify g f x c Find and simplify f x g x

cone hemisphere frustum rectangular pyramid rectangular prism triangular prism cylinder prism with octogonal base

KL is tangent to the unit circle at point T A tanx K D cosecx X m TOL x Accordingly ITLI is equivalent to which of the following T B secx E cotx C sinx

2 Find FD 4 Find US 6 Find MN at appear to be tangent are C 15 F 3x 5 U 3x 1 T 8 12 8 E R 42 D x 11 30 2x 7 S N M

Lesson 5 Splitting Triangle Sides with Dilation Part 1 Cool Down Missing Length What must be true about segment MN 2 C N 1 A 1 8 M 6 3 6 B I

The angles of triangle ABC are in the ratio of 8 3 4 What is the measure of the smallest O 12 O 24 O 36 O 72

The measure of angle Q is 75 degrees What is the measure of angle P R O40 O 70 30 110 P 1p

By Whether you could prove the triangles congruent using Side Side Side Triangle Congruence Theorem Side Angle Side Triangle Congruence Theorem Angle Side Angle Triangle Congruence Theorem None of the above 1 Triangle ABD is congruent to triangle ACD 2 Triangle EJH is congruent to triangle FIH A 3 Triangle LKN is congruent to triangle MKN D

b CH alpha a is alpha is beta is gamma a beta Given a triangle ABC with y 90 B 36 and a 12 find the values of the remaining parts of the triangle gamma B degrees Round all answers to 2 places after the decimal point Give angles in degrees but do not type degrees or any units after any of your answers Submit Question

For the right triangles below find the values of the side lengths a and c Round your answers to the nearest tenth 45 a a 0 C 45 7 X 60 5 30 8

AB BG AC GC LABC LGBC G B T 1 What rigid transformation will take triangle GBC onto triangle ABC 2 Explain why G will coincide with A 3 Is triangle GBC congruent to triangle ABC Explain your reasoning

0 0 AA O yes ASA O not congruent O yes SAS 00 00 00 05

A x 70 76 A x 70 76 41 Show Your Work 41 B O 187 O 63 7 7

What is csc ZA Reduce fractional answers to lowest terms A 12 5 13 B

If the ratio for the sin Z 7071 what is the m Z Hint Use the trig table to determine this measure m Z

Which of the following has a ratio that is equal to b c a Select all that apply a b d 70 e f sin 20 cos 20 tan 20 sin 70 cos 70 tan 70 C b 20

What is cot ZB Reduce fractional answers to lowest terms 10 21 26 C

Triangle PQR is shown where ST is parallel to RQ 1 ST I RQ 2 ZPST ZR and ZPTS ZQ 3 APQR APTS 4 5 PR PS SR PQ PT TQ 6 PS SR PS B Statements 7 PS ST 8 SB TO TQ PS PT TQ PT B PT Reason 3 Select R Statement 4 Select Reason 4 Select 1 Given 2 If two parallel lines are cut by a transversal then corresponding angles are congruent 3 SR Maria wants to prove that PS Select a statement or reason in each blank to complete Maria s proof 4 5 Segment addition postulate 6 Substitution Reasons 7 Commutative property of addition 8 Subtraction property of equality TQ PT

For a given arithmetic sequence the first term a is equal to 18 and the 40th term 940 is equal to 17 Find the value of the 10th term a10 a C

Identify the ratio for the cos Q Write your fraction in simpliest form P 14 R 50 Q

Triangle ABC is shown Statements 1 Triangle ABC is isosceles D is the midpoint of AC 2 2 AD DC 3 3 BABC 4 4 BD exists A 5 5 BD BD 6 6 AABD ACBD 7 7 2BAC ZBCA 1 Given Reasons 2 Definition of midpoint 3 Definition of isosceles triangle 4 A single line segment can be drawn between any two points 5 6 7

7 Use sine or cosine to find height of the pole C 50 52 ft The pole is about A B X x feet tall rounded to the nearest tenth

pende paper Find all missing sides and angles using the law of 14 0 120 2 S

Independent paper worsheet 3 Find all missing sides and angles using the 14 0 120 a law of

For parallelogram MNPQ find the following Q M 12 R 11 10 P 6 5 N Given PQ 28 QM 19 MN 4x 1 QR 17 Find 34 x 35 MN 36 NP 37 RN 38 QN

B For square ABCD find the following A 3 5 6 12 11 10 09 7 2 8 D C Given AD 20 Find 49 DC 50 AC 51 mz1 52 m 12

Right In the accompanying diagram AB is tangent to circle O and secant AD 3 points each 15 If AB 4 and AD 8 find AC A 8 16 If AB 9 and AD 27 find AC B 0 is best described as a

Lesson Applying Trigonometric Functions to Solve for Missing Example In the diagram below AABC is a right triangle If zB is a right angle m C 44 and BC 12 Determine the length of AC to the nearest tenth Hyp A Opp B 44 C 12 Adj C

Right triangle DEF is shown below with the dimensions given in units D Select one O 20 F Which measurement is closest to the value of x in units O 14 9 O 4 8 13 2 14 5 1 E X

Right Triangle Trigonometry Question 1 The dimensions of A QRS shown below are in units Select one 81 O 15 S 9 Which ratio represents the value of sin Q O 7 2 3 4 3 5 Q 5 3 12 R

house to her school Select one 81 37 O 13 Cindy s House What is the approximate measure of the angle in degrees formed by Main Street and Broadway 53 5 blocks Broadway 75 Main Street 4 blocks School 3 blocks

Select one De What is the length c of the right triangle rounded to the nearest tenth O O 71 2 1 3 6 5 8 6 1 2

A guide pai and is staked 6 feet from the base of the tree as shown below Select one a a 32 K 6 ft What is the length to the nearest tenth of a foot of the guide wire from the ground to the palm tree O 8 5 feet O 9 6 feet a O 7 1 feet 11 3 feet

Right Triangle Trigonometry Question 5 What is the value of cos A in the diagram Select one a 60 61 0 60 19 B C 61 60

Right Triangle Trigonometry Question 9 What is the length x of the right triangle rounded to the nearest tenth Select one 1 48 64 98 4 O 109 5 X

12 MP 10 PQ 20 4 MN 9 NQ 12 MP 12 and PR 16 I 8 In right triangle LMN shown below altitude MK is drawn to LN from M If LM 12 and LK 10 the which of the following is the length of KN N 1 2 8 2 4 4 3 6 2 4 14 4 25 L Q 10 12 K COMMON CORE GEOMETRY UNIT ASSESSMENTS UNIT 7 FORM A R M

5 6 U1 U3 U U3 ul U6 U4 U5 tt4 U2 U7 U6 U5 V3 V1 V6 V3 V4 V2 V1 V6 5 V2 V7 V5

The figure shows AABC ADEF with side lengths as indicated x a F 5 E A 9 D 27 21 C X B

KLMJ is a kite Find the values of x and y J 52 K TI The value of x is I The value of y is I I 1 I M X yo L degrees degree

the A The Are finish 30 G AF G H U the 760 below simvikar similarity lilarity statement below 42 triangles are 8 760 F It 21 not similar If so So AFGH Av VW AFGH AW vu F G H AVUW

14 Find X Y the missing Y 9 variables options 3 6 10 4 8 14 3

which triangle is similar to the giver A B 168 C 186 2 por 28 81 to the giver triangle gr B

Prove triangle ABC is congruent to triangle DEF F 5 4 3 2 1 y 3 V A 1 1 N 2 3 4 5 B2 C 3 LLI E D

The diagram shows rectangles 1 2 3 and 4 8 8ft 12 B GFH et 3 loft 2 4 6ft 8 5ff Bft which rectangles are similar ADrectangles 2 and 3 B rectangles 3 and 4 co rectangles 3 and 4

Part A Draw a sketch of a line that appears parallel to and that passes through E Write the degree measure of the rotation you would use if you were creating this line by using a rotation about F Draw your answer in the box D Scroll down to see more

Consider AAXN shown below Which of these is correct 12 18 BODENK If XY and AN are perpendicular then XY is an altitude of AAXN O If XY and AN are congruent then XY is an altitude of AAXN OXY is a midsegment of AAXN because XY connects the midpoints of two sides of the triangle XY is a median of AAXN because XY connects a vertex to the midpoint of the opposite side of a t

Select one Similarity Question 4 What value of x would make A PQR A MNL a O O 10 cm O 15 cm R 16 cm 14 cm 12 cm 16 cm Q M 1 18 cm 24 cm N