Solution of triangles Questions and Answers

4 Listen What is the indicated missing angle 9 24

What is the reason for 5 Given Line I is an auxiliary line parallel to m Prove m2 m24 m2 5 180 D 3 4 2 m 1 m2 4 Statements 1 Line I is an auxiliary line parallel to m 4 DBC m2 3 180 5 m 1 B 1 m 2 DBC 2 3 1 5 3 E C Reasons 1 Given 2 Alternate Interior Angle Theorem 3 Alternate Interior Angle Theorem 4 Linear Pair Postulate 5

What is reason 3 Given M is the midpoint of AB and AB LCM Prove AC BC C A M Statements 1 M is the midpoint of AB 2 AB LCM 3 AM BM 5 B 4 ZAMCZ BCM 6 AAMC ABMC 7 AC BC Reasons 1 Given 2 Given 3 4 Right Angle Congruence Theorem 5 Reflexive Property 6 SAS 7

Sarah said that the reason for 2 is Vertical Angles which is incorrect Why can t they be vertical angles What is the correct answer Complete the proof that mZVUW m2PRS 180 1 2 3 S P R Statement QS TV ZVUW ZSRU U m2PRS m2SRU 180 W CYLIN m PRS 180 T Reason Given Angles forming a linear pair sum to 180

What is the reason for 3 Complete the proof that ZTWV ZUTW 1 2 3 4 Y Statement W 1 SU VX ZTWV ZRTS ZRTS ZUTW ZTWV ZUTW T X R Reason Given

Listen Find the value of the highlighted angle 13x1 11x 13

8 8 11 14 9 12 15 4 Listen Triangle KLM is the pre image of A K L M before a transformation 18 16 14 12 10 8 6 4 K Part A Timothy said that triangle KLM was dilated by a scale factor of 1 5 centered at the origin Is Timothy correct Explain your answer or show your work nimdar Explain

Solve for DG Show all work using the equation editor 24 F 3044 32 E 40 D G

3 a 6 9 1 12 15 1 What type of segment is KL K Altitude Midsegment Median Perpendicular Bisector L

What is the reason for 3 Given A ACE with medians CF and EB Prove 3 medians intersect at point G The Centroid Statement H 3 BG CD BG CD D Reason 1 In AACD B and G are the 1 midpoints of sides AC and AD In AAED F and G are midpoints 2 BG and FG are midsegments 2 3

Listen Are they similar If so by which postulate 36 N L 63 W U 24 40 42 M 70 A

Thangle XYZ is shown on the coordinate plane 8 6 O 6 2 4 O 8 2 10 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10 X po 2 4 Z 6 8 Y If triangle XYZ is translated using the rule x y x 2 y 3 and then reflected across the x axis to create triangle X Y Z what is the location of Z O 2 8 10

What is the value of sin c sin C A 13 12 C 5 B

Listen Solve for the missing side Show all work 11 23 X

Listen What is the value of x y 60 X 3

In the figure AC is a diameter of the circle CG bisects ACB with G on AB GF 1 AC with F on AC AD GC 1 2 Prove that 9 1 1 ACAD is isosceles 9 1 2 9 1 3 D BC BG AC GA AAFG AABC 9 2 1 AB A F C G B If BC 12 units and the radius of the circle is 10 units calculate the length of

Which statement is sufficient evidence that ADEF is congruent to AABCP B C F 1 AB DE and BC EF 2 LD LA LB LE LC LF 3 There is a sequence of rigid motions that maps AB onto DE BC onto EF and AC onto DF 4 There is a sequence of rigid motions that maps point A onto point D AB onto DE and LB onto ZE

What is the value of x 02 06 O 12 24 36 12

U Given A B C and point D not collinear with A B and C Figure 5 17 Prove that AB BC Figure 5 17 AD sin CD sin ADB CDB AC AD sin ADC BC BD sin XBDC Hint Use the law of sines to compute AB AD CD BC and BD BC and remember that sin ABD sin CBD B

Type the correct answer in the box 5 cm 5 cm 12 cm A rectangular prism has a height of 12 centimeters and a square base with sides measuring 5 centimeters A pyramid with the same base and half the height of the prism is placed inside the prism as shown in the figure The volume of the space outside the pyramid but inside the prism is cubic centimeters

Find the surface area of the cone in terms of 60 cm Not drawn to scale 2 111 cm 55 5 cm 2 3 2 O 57 cm R 17 cm 2 3 cm

The polygons are similar but not necessarily drawn to scale Find the value of x A 5x B 4 C 04 O 20 5 01 D

Find the area of the circle Leave your answer in terms of 4 1 m 2 4 2025 m 8 405 m O 11 2 m 16 81 m

Use the Law of Cosines to determine the indicated side x Assume b 14 and c 18 Round your answer to one decimal place C b c a Step 1 The Law of Cosines states that for the triangle ABC with sides a b and c b 108 a 18 x 14 B 324 196 In the given triangle you know sides b and c and angle A and need to find a So you can rewrite this formula a c b 6 cos A Step 2 Substitute known values into the alternate form of the Law of Cosines Round your answer to three decimal places a 2 b 2ab cos A 2 2 2ab 28 14 2bc cos C 1 18 cos 108 1x cos 108

Which theorem or postulate proves the two triangles are similar 20 19 7615 Not drawn to scale O SA Postulate O SSS Theorem OAA Postulate 16

What is the value of x x 5 O 10 O 7 5 O 2 5 X 2 x 1

Qu GivensABC A B C midpoint of the sives respectively let O the perpendicular from it onto L M B a let feet of the onto bisects 6 Compute the angle between OmJ 13 c P be the BC CA ond var be the foot of BC be the respective perpendiculars from D C A A B prove that ADJ 28 12 3 U LM

5 In the accompanying diagram of quadrilateral QRST LRST SRLQR and ST 1QT Prove QR QR QT QT is the angle bisector of R T S

Jed is working on stained glass project and needs to draw a triangle with side of 7 11 and 15 inches out of lead cane to enclosed the glass is the largest angle he needs to create using leading cane

Find the value of the variable in the isosceles trapezoid X 61 3x 10

Find the value of x Round the length to the nearest tenth 22 16 m Not drawn to scale O 14 8 m 6m 6 5 m 42 7 m X

Green Township to the main road Expressway East so that drivers can travel between Green Township and Metro City in the shortest possible time The direct north south distance from Green Township to Expressway East is 35 miles and the total east west distance between Metro City and the point directly south of Green Township on Expressway East is 70 miles See diagram which is for illustrative purposes only and not to scale 35 70 Al The speed limit on the new road will be 35 mph and the speed limit on Expressway East is 60 mph a How far to the west of Metro City should the new road from Green Township connect to Expressway East to enable drivers to make the trip in the least amount of time If necessary round result to 1 decimal place miles b What is the total time that the trip from Township to Metro City will take If necessary round result to 1 decimal place

Write the ratios for sin A and cos A A 10 sin A Not drawn to scale sin A sin A 26 sin A 24 10 26 24 10 24 26 24 B cos A cos A cos A cos A 24 26 10 26 10 24 10 26

A slide 4 1 meters long makes an angle of 350 with the ground To the nearest tenth of a meter how far above the ground is the top of the slide X 07 1 m 2 4 m 3 4 m O 5 0 m 4 1 m 35

Find the value of x and y rounded to the nearest tenth X 45 y 34 30 x 24 0 y 139 3 Ox 24 0 y 46 4 x 48 1 y 46 4 x 48 1 y 139 3

Match each scatterplot shown below with one of the four specified correlations 0800 O OOO 00 88888 00 a Q a 0 99 b 0 26 c 0 12 d 0 82

O is the midpoint of circle CHEF EH is extended and cuts the circle CGEO at G CFE x 10 1 10 2 10 3 10 4 Prove that 180 2x Prove that EF CH Prove that ACGH AFGE N N E If EH HG 5 3 determine the value of EF HC X 1

In triangle ABC ZA is a right angle and mZB 45 Find BC If your answer is not an integer leave it in simplest radical form O 10 2 ft B A Not drawn to scale O 20 ft O 10 ft C O 20 2 ft 10 ft

4 Given SABC A B C be the midpoint of the Si des BC CA ond AB respectively and let D be the foot of the perpendiculur from A onto BC a Let Lim that perpendiculos from b Compute be B bisects the respective P feet of the O oto C A A B Prove AD this is not I between Lm the engle and BC

Prove that the triangles on the grid below are congruent by using the following methods 1 SSS 2 SAS Explain all of your reasoning CO O E

O False Question 6 1 5 pt In any situation three kinds of implications may be involved possible ones probable ones and impossible ones

bisects ZEDG Find FG The DF diagram is not to scale D O 14 O 19 2 E n 8 3n 4

40 Find the value of x 5 5I2 A 1 5 B 4 2 C 6 D 2 8 3 X

Find the value of x Round to the nearest tenth O 10 2 O 14 5 O 14 2 O 10 7 12 32 Not drawn to scale

Pyramid A has a volume of 10 cubic units a height of 5 units and a length of 9 units for the longest edge Pyramid B has the same base area and height but a length of 7 units for the longest edge LO 9 A 7 B What is the volume of pyramid B

What is the value of x given that PQ BC B O 20 O 24 8 0 De P A 12 18

LO bisects NLM LM 18 NO 4 and LN 10 What is the value of X L O 45 07 2 O 5 43 N M

3 In the accompanying diagram PA is tangent to circle O at A chord AC and secant PCED are drawn and chords AOB and CD intersect at E If mAD 130 and m BAC 50 find m P m BEC and m PCA D B E A C P

Writing Exponential Equations Andrew purchases a new home for 175 000 Write an equation for V the value of the house after n years assuming that the value changes in the following ways V Increases by 7 every year Decreases by 6 every year Increases by 5 every 4 years Decreases by 8 every 3 years Decreases by 1 every 6 months twice each year Increases by 2 every month 12 times each year 175000 1 0 07 x 175000 1 0 06 x V 175000 1 0 05 x 3 175000 1 0 08 x 175000 1 0 01 x 12 V 175000 1 0 02 2 x V V V HINT To enter an expression like 25 0 8 2 be sure to put parentheses around the exponent 25 0 8 2x To enter an expression like 25 0 8 be sure to put parentheses around the exponent 25 0 8 x 2

R S and T are the vertices of one triangle E F and D are the vertices of another triangle m R 60 m S 80 m F 60 m D 40 RS 4 and EF 4 Are the two triangles congruent If yes explain and tell which segment is congruent to RT yes by AAS ED O yes by SAS ED O No the two triangles are not congruent O yes by ASA FD