Geometry Questions

What is the equivalent trig ratio to sin 25 cos 25 tan 25 sin 65 cos 65 O

You are riding the Ferris wheel at the fair You look down at your friends in line for the next ride at an angle of depression of 40 degrees The Ferris wheel is 192 feet tall What is the horizontal distance you need to walk to your friends when you get off the Ferris wheel 228 8 feet 94 2 feet 354 9 feet 179 7 feet

It is believed the best angle to fly a kite is 45 If you fly a kite at this angle and let out 225 feet of string approximately how high above the ground will the kite be Use the diagram below to answer the question 225 ft 45 not drawn to scale O260 feet

b Which of the two interpretations from part a can help us make sense of an angle measure of 450 Explain c Jeffrey measures ABC with a protractor and says the angle is 130 Is he correct Why or why not

Name the quadrant in which the angle lies cos 0 tan 0 0 Choose the correct answer below O Quadrant II O Quadrant I O Quadrant III Quadrant IV

Use the fundamental trigonometric identities to simplify the expression There is more th 2 sec x 1 sin x Step 1 Begin by distributing sec x over r 1 sin x 2 sec x 1 sin x 2 sec x sin x

Draw a picture of the angle in standard position labeling x and y axis initial and terminal side a curved arrow with the quadrants labeled Use the Pythagorean Identity to calculate the sine or cosine of the angle 0 Determine if sine and cosine are positive or negative in this quadrant cos 0 2 7 and is between 270 and 360 tan 0 To enter a square root type sqrt To enter x type pi To enter a fraction type Select an answer Select an answer

A directed line segment from A 2 2 to B is divided into the ratio 4 2 by P 4 67 2 What is the coordiantes of B

What is the measure of the indicated missing angle 29 23

An object dropped from the top of the Leaning Tower of Pisa lands 17 feet from the base 179 ft 17 ft Note The figure is not drawn to scale Which of these equations should be used to determine the angle x that the Leaning Tower of Pisa makes with the ground

A 20 meter long cable is used to support a telephone pole holding it perpendicular to the ground If the cable forms a 60 angle with the ground how high up the pole should the cable be attached 10 meters 20 3 meters 20 2 meters 10 3 meters

The degree measure of an angle in a right triangle is x You are given that sin x 3 Which of these expressions is also equal to 0 a cos x 45 b cos 60 x c cos x d cos 90 x e cos 45 x

Listen A 45 ft ladder is leaning up against a building The base of the ladder is 20 feet away from the building What is the angle of elevation to the top of the building Round to the nearest degree 38 21 64 57 11

Listen What is the equivalent trig ratio to cos 42 O sin 48 sin 42 Ocos 48 Otan 42

Listen What is the measure of the indicated missing angle 24 37

What is the indicated missing angle 35 62 49 28 25 22

4 Listen What is the indicated missing angle 9 24

Given quadrilateral A 2 1 B 1 3 C 6 5 D 7 1 you want to prove that it is a parallelogram by showing opposite sides are parallel What formula would you use Show that AB is parallel to CD Show all work

Johnny is wanting to prove that parallelogram ABCD is a rectangle He shows that opposite sides are congruent and opposite sides are parallel Can he conclude ABCD is a rectangle Why or why not Explain your reasoning in complete sentences

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

Solve for x 6 4x W H U x 4 S Ox 10 Ox 4 Ox 1 Ox 7 R V

Parallelogram ABCD is shown below D C B Which pair of triangles can be established to be congruent to prove that ZDAB ZBCD A DAB and A BCD A AED and A BEC A ADC and A BCD A DEC and A BEA

Given AB CB BM LAC and M is the midpoint of AC Prove A C B A M C Statements 1 AB CB 2 BM LAC 3 M is the midpoint of AC 4 AMB Z CMB 5 AM CM 6 AAMB ACMB 7 A C Reasons 1 Given 2 Given 3 Given 4 Right Angle Congruence Theorem 5 6 7

Given the quadrilateral is a parallelogram solve for x L K 10x 10 I Ox 20 Ox 4 Ox 7 x 10 N

What could be shown about the diagonals of parallelogram PQRS to complete the proof that diagonals of a parallelogram bisect each other P r t BI R s 0 S 0 0 r s t PR is a perpendicular bisector of SQ Angles formed by the intersection of PR and SQ each measure 90 PR and SQ have the same midpoint RR and So have the same length

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

What is the length of RS V R W X 3 x 5 S X

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

Listen What is the mZG F 20 G H

Given lines n and r are parallel 22 and 2 7 are P 1 2 3 4 5 7 6 8 n r

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

What is the reason for 4 Proof of the Pythagorean Theorem Given Triangle ABC is a right Triangle and CD is an altitude Prove a b c Statement 1 Triangle ABC is a right Triangle and 1 CD is an altitude 2 m BDC 90 mzADC 90 3 m A m A 4 m B m B 5 m ACB m CDB m ADC 6 AACB ACDB AADC 7 b 1 a b c 10 C e Reason a 2 3 4 5 6 7 B

Once the construction below is complete creating a parallel line to PS through point Q which of the reasons listed contribute to proving the validity of the construction P P Q W T To T O When two lines are cut by a transversal and the vertical angles are congruent the lines are parallel Definition of segment bisector When two lines are cut by a transversal and the correspondina anales are Sign out

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

Given A ABC with points A 1 2 B 4 3 and C 0 0 dilated about a center at the origin by a scale factor of 3 an c

The figure shows the results of a construction of the bisector of ZP Order the following steps for this construction using the numbers 1 4 Ex the first step is 1 second step is 2 and so on V Using a straightedge draw the line through P and X Name the intersection of the two arcs X Draw an arc centered at P to create points Y and A Draw two intersecting arcs with the same radius one centered at Y and one centered at A on the interior of ZP

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

Find the length of an arc that subtends a central angle of 310 in a circle of radius 7 km arc length km Answer must be exact Use pi for and enter answer using a reduced fraction

One way to show that two triangles are similar is to show that two angles of one are congruent to two angles of the other an angle of one is congruent to an angle of the other a side of one is congruent to a side of the other two sides of one are proportional to two sides of the other

A tree with a height of 22 ft casts a shadow 5 ft long on the ground How high is another tree that casts a shadow which is 2 ft long 11 4 ft 8 8 ft 2 5 ft 6 3 ft

Write a similarity statement for the following triangles Be sure to match up the correct corresponding proportional sides M 6 N O

Solve for x Remember to match up corresponding parts by the similarity statement ADCBATSR C T 38 21 33 R 15x 11 Ox 11 x 21 x 17 x 8 B 38 98 S D

What is the reason for 9 Given ABCA where E is the midpoint of AC and D is the midpoint of BA Prove DE BC and that BC DE Statement 1 D is the midpoint of AB E is the midpoint of AC 2 MAD mDB MAE mEB 3 mzA mZA 4 AD DB AB AE EC AC 5 AD AD AB AE AE AC B 6 2 AD AB 2 AE AC Reason 1 2 3 4 C 5 6 Simplify

What is the reason for 4 Given DE BC Prove AD AB DB EC Statement 1 DE BC 2 mzA mZA 3 m AED m ACB 4 AACB AAED AD 5 AB AE EC 6 AD DB AB AF FC AG B Reason 1 2 3 4 5 6

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

Listen What is the reason for 4 Prove Corresponding Angles 7 5 3 8 1 6 2 m n Given 23 and 27 are corresponding angles Prove 43 27 Statements 1 23 and 27 are corresponding angles 2 3 26 27 4 3 27 Reasons 1 2 3 Vertical Angles Congruency Theorem 4

Listen What is the reason for 4 Given CB AD and CBI AD H B A Statements 1 CB AD 2 CB AD 3 4CBD ADB 4 BD BD 5 ABCD ADAB Reasons