Solution of triangles Questions and Answers

which triangle AD 24 IS similar to the given triangle Do 16 13

Select the correct answers from each drop down menu Triangle XYZ has an altitude as shown Eric and Maggie are both trying to prove the law of sines X Eric s Work h sin X h Y h h and sin Z Z h1 Maggie s Work h and sin X 7 24 ysin X The proof was correctly started by The next step in the proof is to sin Y zsin X and h1 Isin Z h sin Y and h2 0 by the

What type of polygon is shown convex heptagon O concave heptagon O concave hexagon O convex hexagon

A T 8 B D S X C Prove the following using the two column proof format GIVEN AB CB and AD CD PROVE AABD ACDB Statements 1 AB CB and AD CD Reasons

of Angle What is the sum of the interior angle measures of a regular decagon What is the measure of each interior angle of a regular decagon Theoren O

Use the figure on the right to find the length of DC 10 D E B

17 Find the value of x 17 A 13 99 O A O B 09 R D 65 M B 10 D 12

11 Find the value of x OA 23 OB 17 OC 11 OD 19 3x 14 5x 8

for each of the following determine if the triangles are congruent if so write the congruent statement give the reason and find x or x and y C A 2Y Y 2X 1 D 5y 3x 1 3y 2x 1 C

In triangle ACE G is the centroid and BE 12 Find BG and G C A B F D by OA BG 6 GE 6 OB BG 8 GE 4 OC BG 3 GE 9 OD BG 4 GE 8

27 Find the values of x and y A B 20 of D Drawing not to scale 47 OA OB x QC x OD x C X x 90 y 47 43 y 47 47 y 43 90 y 43

15 Write the tangent ratios for P and C P 21 R 29 20 Not drawn to scale OA OB tan P tan P OC tan P OD tan P 29 21 20 21 21 20 29 20 tan Q tan Q tan Q tan Q 21 29 21 20 20 21 20 29

The measure of the arc from B to A not passing thru C is 30 degrees What is the measure of angle BOA What is the measure of angle BDA D there is a Desmos slide in the lesson where you can draw on this same picture as needed What is the measure of angle BCA degrees degrees B degrees A

3 Joe constructed perpendicular bisectors of two sides of a triangle What is his next step if he is constructing a circle circumscribing a triangle O Draw arcs above and below the perpendicular bisector on one side Find the angle bisectors of two angles Mark the intersection of the perpendicular bisectors Draw a line from the midpoint of one side to the opposite angle of the triangle

Round your answer to the nearest hundredth 6 7 DO

Refer to OJ for problems 9 11 Segment KL is tangent to OJ A M L If the radius is 3 and LM 2 what is KL Answer

AGHI circumscribes OK What is the perimeter of A GHI 5 in G K 2 in 6 in H

3 Use the parallelogram to complete the stateme E G F 20 in 3 The measure of ZF a 40 b 50 D 40 A 10 in c 140 d 150 zoom in 3 O A B Oc D

5 Find the perimeter of ADEF 19 J 16 40 E

Find the value of each variable in the circle to the right The dot represents the center of the circle a Simplify your answer Do not include the degree symbol in your answer

a right triangle has an area of 20 square centimetes and a hypotenus of 10 cm what are the exact lengths of the legs of the right triangle

In triangle ABC shown the side from A to B is 50m long while ZABC 1000 and ZACB 300 Find the measure of angle BAC

1 The volumes of two similar figures are given The surface area of the smaller figure is given Find the surface area of the larger figure Show your work V 27 cm V 125 cm SA 63 in

Cool Down Are Label each example with one of the statements The triangles must be congruent The triangles might not be congruent 1 HJLJE HILIE HJ HI E 1 Triangle EJH and triangle EIH 2 AF AD ZF ZD

There are 800 toothpicks in a regular sized box If a jumbo box is made by doubling all the dimensions of the regular sized box how many toothpicks will the jumbo box hold The jumbo box holds toothpicks

12 Ms Senter and her class want to design a Red Wolves Sign for the classroom it will be an isosceles triangle with base angles that are 2 times and 3 additional degrees bigger than the top angle to determine the angles of the triangular sign hint drawing a picture may help

8 Can these sides make a triangle a 3 6 9 b c 3 7 8 20 25 40

Find the circumference and area of the circle Use the key for x Circle of radius 8 ft The circumference of the circle is approximately Type an integer or decimal rounded to the nearest t ft 4 d

26 mR 27 Find m40 The figure is not d to scale 27 m2BOC 69 Find the measure of ZBAC The figure is not drawn to scale 69

Find two angles between 0 and 2 such that sin 0 0 49 Start by drawing a sketch Enter your answers as a comma separated list Note that all solutions should be in radians 0 0 51208 179 48792 help numbers Find two angles between 0 and 2m such that cos 0 0 36 Start by drawing a sketch Enter your answers as a comma separated list Note that all solutions should be in radians 0 1 9390 4 344 help numbers

3 If sin x 20 cosx the value of x is

Question 8 Triangle XYZ is located in the first quadrant of the coordinate plane If this triangle is reflected over the y axis what is true about the vertices of the reflection A B C D The x values are negative and the y values are positive The x values are positive and the y values are negative The x and y values are positive The x and y values are negative

Date Question 1 Equilateral AJKL has a median of 40 3 centimeters as shown in the figure below A 05 12 B What is the perimeter of AJKL in centimeters D 40 80 C 240 ur 1600 K 40 13 EL S L

The diagram shows the graph of a parabola and it s key parts What do you call point B in the diagram C B

REASONING Is it possible for AJKL and AXYZ to be similar when m J 71 m K 52 m X 71 and m Z 57 Ex your reasoning O No ZK and ZZ are not congruent O Yes corresponding angles are congruent O No all three angles for each triangle are not given OYes the largest angles of each triangle are congruent

Determine whether the triangles are similar If they are select the correct similarity statel 40 AV 55 N O similar ALMN AWXY O similar ALMN AYXW Osimilar AMNL AXYW not similar 3

What are the values of the trigonometric ratios for this triangle Drag the answers into the boxes sin 0 cos tan 0 III 0 13 12 5

The figures to the right are similar Compare the first figure to the second Give the ratio of the perimeters and the ratio of the areas The ratio of the perimeters is Type an integer or a simplified fraction 18 cm 27 cm

9 Solve for the each length Round to the nearest tenth when needed P 6 a QP S 30 R bQS c QR

Line segment ON is perpendicular to line segment ML Line segment OM 13 units in length line segment PN 8 units in length M 13 O 8 Q N L What is the length of chord ML O 20 units O24 units 26 units O 30 units

L 8 8 5 M P The measure of central angle LOP is The length of LP is The length of MP is units units 0

G Z E U 4 Explain the relationship between point Z and the triangle Justify with the applicable theorem 5 If the length of GU is 18 units what is the length of GZ Show all your calculations and unit measurements 6 If the length of ZT is 4 8 units what is the length of OT Show all your calculations and unit measurements

4 72 M N What is the ratio of the sector area to the area of th entire circle 00 0 2 04

3r D If tan 0 37 2 a sin 20 FORMULA IS BELOW sin 20 2 sin 8 cos 24 37 find the exact value of each of the following a sin 20 on an exact answer using radicals as needed

Let sinA 12 13 with A in QIV and cosB 3 5 with B in QI Answer exactly

1 Points A and B are on opposite sides of the Grand Canyon Point C is 200 yards from Point A on the same side of the canyon Angle B measures 87 and angle C measures 67 What are the distances between the points

Triangle Similarity Find the missing length The triangles in each pair are similar 1 ASTU ALKJ 2 S H 24 D L 3 ATSR ATGH C 45 G 27 5 ARQP ACDE K T Q 56 E ZV 59 42 U P 59 98 110 4 AWVU AWCD 168 A A 8 T 16 140 60 R T U E 15 30 6 AUTS AABC B 41 U T 41 110 20 F 10 D A S V C

Circle O is inscribed in the given triangle 12 P 4 O R 6 What is the perimeter of the triangle O22 units O 30 units O 44 units O 60 units

Use the given information and a calculator to find 0 to the nearest tenth of a degree if 0 0 360 cos 0 0 3150 with 0 in QIII sin 0 0 3168 with 0 in QIII sec 0 2 with 8 in QII sin 8 3 2 and 0 in QIV

Given Diagram as shown h 24 b 30 c 25 Find a K R r note K area triangle ABC B C h A D b R