Solution of triangles Questions and Answers

Which of the following statements must be true based on the diagram below Select all that apply Diagram is not to scale K L H J M I LM is a segment bisector OLM is a perpendicular bisector DM is the vertex of a pair of congruent angles in the diagram L is the midpoint of a segment in the diagram M is the midpoint of a segment in the diagram None of the above 4

PROPERTI AND CONGRUENCE m l m 2 m 5 m 2 m 3 m 2 m 7 m 3 m 7 Remember In order to use the Transitive Property the equivalent parts must each be an ENTIRE SIDE of the equation W Transitive Property of Equality Symmetric Property of m l m 3 m 5 m 2 m 3 Note In a real proof it would not really be very helpful to end up back where we started but we are just practicing using the properties to justify each step 4

3 5 A triangle is formed with the points 1 5 1 8 and 5 5 What is the area and perimeter of the triangle

D Given each trigonometric ratio determine all values of 0 to the nearest degree if 0 0 360 Sketch all possible angles on the Cartesian plane b sin 5 8 sec 8 1 3 2 5

Ron wants to build a ramp with a length of 14 ft and an angle of elevation of 26 The height of the ramp is about feet C 26 Part B 14 ft y x B Note Round your answer to the nearest tenth The length of the base of the ramp is about Note Round your answer to the nearest tenth feet

The point of concurrency of the angle bisectors of a triangle is called the OA median B D circumcenter concurrent incenter of the triang

Complete the statement LABC P A OA MNP OB 4PMN OC NMP OD 4NPM B

Which triangles are congruent by ASA T U H OA AHGF and ATVU OB AVTU and AABC OC None of these D AVTU and A HGF F A B

L Name the angle included by the sides NM and MP N P OA ZP OB ZN OC ZM OD None of these M

Fill in the missing information AMNO APQR M 59 a ZN Z b 20 4 68 OA ZR 20 OB 40 LR OC LP LR OD 20 LP 53 N P R Q

The figures below are similar Which of the following is true about the corresponding sides B L D Congruent Equal N O Proportional Parallel No Relationship T A H F

Determine if the triangles below are similar and which similarity postulate applies W Similar by AA Similar by SSS O Similar by SAS X Y P Z

The perimeter of a square is 366 What is the length of its diagonal T

Solve the right triangle X 45 3 6 YZ XY mZZ Y Write your answers in simplified rationalized form Do not rou O Z

Find mZR R mZR 3 S Write your answer as an integer or as a decimal rounded to the nearest te T O 2

H 9 HI mZH m2I J DO Write your answers in simplified rationalized form Do not round 9 O I

Solve the right triangle H I HJ HI mZH 30 B 66 Write your answers in simplified rationalized form Do not roun J

Problems on your own and show your work A 5 in 6 in 1 3 5 4m 4 5 m 10 m 6 ft 7 ft 7 an octagon with an apothem 4 8 centimeters long and a side 4 centimeters long 4 cm 2 10 cm 4 6 12 km 13 cm 12 km 8 2 cm 10 19 cm Find the area of the shaded region in each regular polygon 9 2 2 m 8 a hexagon with a side 23 1 meters long and an apothem 20 0 meters long 3 m 6 ft 20 ft

Priya is teaching her younger cousin to ride a bike She wants to stay on roads that are not too steep and easy enough for a new bike rider She has decided the roads must have an angle less than or equal to 7 degrees A 7 degree angle in a right triangle has a 3 25 ratio for the legs Select the legs of all right triangles that would be safe for a new bike rider

Given the information below determine the value of X X 11x 11 D 30 E 25 21 A F 77 B AABC AFED To set up your proportion corresponding sides go in the same fraction and parts from the same triangle go in the same location of the fractions both in the numerator top or both in the denominator bottom Use the similarity statement to determine the corresponding sides Remember the order of

also select the reasoning for your answer 33 21 Answer 1 not similar Answer 2 27 Answer 3 18 not congruent Answer 4 The figures are not similar because the corresponding angles are not congruent and the corresponding sides are not enough information A STU Ano similarity statement S 30 22 not enough information B T

Which postulate theorem proves the triangles similar if B A C OSAS E Not Similar D

Ex 5 Graph AB with endpoints A 4 4 and B 1 7 Graph its image after the composition 6 4 q 8 64 2 36 6 Translation x y x 2 y 1 Rotation 270 about the origin

In the triangle ABC side b 9 side c 7 and side a 6 what is the value of the cos A Round your answer to the nearest hundredth b B picture of triangle is purely for labeling use angles and side lengths specified in the problem

Fill in the blanks to describe the transformations that occur in the the graph from the Parent Function to the Graph Note this is set up exactly the same as in your lesson so you should be using the same language wording as you learned in the lesson Graph Parent Direction Vertex Opening

S P U PU 7 UV 3 PV 9 Complete the sentences The length of UR is Select The length of VQ is Select The length of VT is Select T 4 R

3 A What is NOT true about the image m ABD m CBD B B 74 C BD is the angle bisector of ZABC AB BC D ZABC ZADC D C 74

Solve the right triangle V U 45 8 TV UV mZT T Vrite your answers in simplified rationalized form Do not roune

Question 1 1 point Name the postulate if possible that makes the triangles congruent T O O O a b C d A H a b C Od SSS ASA AAS SSS Question 2 1 point Name the postulate if possible that makes the triangles congruent R T S SAS AAS ASA Not Possible A A E M B P Question 3 1 point Name the postulate if possible that makes the triangles congruent

Find BD B C BD 36 Write your answer as an integer or as a decimal rounded to the nearest ter

14 Given Quadrilateral ABCD with vertices A 2 3 B 1 1 C 1 2 and D 0 4 ove ABCD is a square

Find sin 8 csc0 and cot0 where is the angle shown in the figure Give exact values not decimal approximations 25 0 24 sin 9 csc 0 cot 0 11 7 0

1 Aiden borrows a book from a public library He read a few pages on day one On day two he reads twice the number of pages than he read on day one On the third day he reads six pages less than what he read on the first day If he read the entire book that contains 458 pages in three days how many pages did he read on day three

A Just Line Symmetry Has Both Symmetries Possible answers M T No Answers Chosen W N 610 No Answers Chosen A 39 Z L Z O 1 point The figure shows overline JN and overline KM intersecting at point L 3x 5 Z Just Point Symmtry X No Answers Chosen N

Find the tangent of ZX 82 X 97 15 010 W Write your answer in simplified rationalized form Do not rou tan X

Is this statement always sometimes or never true If ZF is a 60 angle then cos F sin F always sometimes never

S 85 00 77 T 36 R Simplify your answer and write it as a proper fraction improper fraction or whole nur sin T

In the following list the angles of the triangle from shortest to longest C Smallest 1 2 27 m 3 18 m A B 24 m angle C angle B angle A

For each triangle check all that apply Triangle A Scalene Isosceles Equilateral 8 18 Triangle B 18 Scalene Isosceles Equilateral 18 1 Triangle C Scalene Isosceles Equilateral 10

Georgia Department of Education Georgia Standards of Excellence Framework GSE Geometry Unit 4 Part 2 The Segment Theorems Graphic Organizer In the remaining items of this task we will work with the relationships between the lengths of the segments created when these lines intersect Picture Type 2 tangents vertex outside 2 secants vertex outside Secant and tangent vertex outside 2 secants VERTEX INSIDE Theorem A

In Exercises 1 and 2 classify the triangle by its sides and by measuring Its angles 2 In Exercises 3 and 4 classify AQRS by its sides 3 Q 2 2 R 1 2 S 4 4 In Exercises 5 8 find the value of x 5 7 63 85 2x 6 4x 18 to 36 4 Q 1 3 R 3 2 S 2 1 1 A5OTAS 8 11 The figure shows the measures of various angles of a roof and its supports Find the measure of 21 the angle between an eave and a horizontal support beam 2x 61 3x 5 9 The measure of one acute angle of a right triangle is 12 more than 3 times the measure of the other acute angle Find the measure of each acute angle of the right triangle 10 Your friend claims that the measure of an exterior angle of a triangle can never be acute because it is the sum of the two nonadjacent angles of the triangle Is your friend correct Explain your reasoning 110

Complete the proof that ZX ZU 1 2 3 4 5 6 9 7 8 U N HHH Statement YZ VW WX UZ UV XY WY VZ V Y VZ YZ VY WY VW VY VZ VW VY AUVZAXYW ZX LU W X Reason Given Given Given Additive Property of Length Substitution Transitive Property of Equality SSS CPCTC

What is the tangent ratio for the angle indicated O 17 8 O 8 15 O8 17 15 17 a 17 15 8

1 Find the m KMU K 4 A L 50 MU Find the value of x 2x 8 C Y 123 3x 5 2 5

26 Metal Brace The diagram shows the dimensions of a metal brace used for strengthening a vertical and horizontal wooden junction Classify the triangle formed by its sides Then copy the triangle measure the angles and classify the triangle by its angles 10 5 in 7 7 in 7 14 in

4 The vertices of quadrilateral ABCD have coordinates A 1 3 B 1 1 C 5 2 and D 3 4 Prove that ABCD is a parallelogram Prove that ABCD is not a rhombus Justify mathematically and explain

Geometry Classwork Review Lessons 4 1 to 4 4 Find each measure 1 mz1 2 3 40 2 m42 40 3 m23 95 4 m24 45 5 m25 95 6 In the Figure AABC AFDE 7 Find the value of y 2x y 180 y 90 8 Find the value of x 2x 90 180 Show that polygons are congruent by identifying all congruent corresponding parts Then write a congruence statement 2x 2 X 1 9 Write a two column proof Given PR DE PT DF LR LE LT LF Prove APRT ADEF Statements 1 PR DE PT DFLR LE LT LF PR DE PBT DEF Name Kinlee 12 8 Date 80 1 108 C 2 48 B D 44 Reasons Period 7 Given 2 Third Angle Theorem 3 Athm 4 105 E 2x y

Triangle ABC is inscribed in a circle with side a 60 cm and angle BAC 20 degrees and angle ABC 40 degrees Find the diameter of the circle

Find the measure of ZBCD in degrees Lesson 5 1 42 B 64

A cruise ship maintains a speed of 19 knots nautical miles per hour sailing from San Juan to Barbados a distance of 600 nautical miles To avoid a tropical storm the captain heads out of San Juan at a direction of 11 off a direct heading to Barbados The captain maintains the 19 knot speed for 11 hours after which time the path to Barbados becomes clear of storms a Through what angle should the captain turn to head directly to Barbados b Once the turn is made how long will it be before the ship reaches Barbados if the same 19 knot speed is maintained Barbados 600 11 San Juan