Geometry
Unit 5
TEST
State the postulate or theorem you would use to prove each pair of triangles congruent. If the triangles cannot be proven congruent, write not enough information.
1.2.3.
4.5.6.
7.8.9.
10.11.
Find the value of x and y.
10.11.
12.13.
14. 15.
14. ∆CGI∆MPR.Nameallofthepairsofcorrespondingcongruentparts.
19.Complete the following proof by providing
the reason for each statement.
Given: 1 2;
Prove: 3 4
Statements / Reasons1) 1 2;
2)
3) ∆WXP ∆ZYP
4)
5) 3 4 / 1)
2)
3)
4)
5)
20.Write a proof for the following:
Given: , D is the midpoint of .
Prove:
1. Twotriangleshavethefollowingpairsofcongruentsides:and
Write the congruence statement for the two triangles.
Use the diagram below. Tell why each statement is true.
10.A C
11.AXBCXD
12.∆ABX∆CDX
10. In∆ABC,whichsideisincludedbetweenBandC?
11. In∆XYZ,isincludedbetweenwhichtwoangles?
Determine what other information you need to prove the two triangles congruent. Then write the congruence statement and name the postulate or theorem you would use.
14. 15.
16. If two triangles are congruent, all their corresponding parts are congruent. Write the converse of this statement. Is the converse true? Explain.
18.Your classmate says the triangles at the right are not congruent by SSS. She explains that congruent sides do not correspond. Explain the error in her reasoning.
Algebra Solve each proportion.
1. 2.
3. Determinewhetherthepolygonsattherightaresimilar. If so, write a similarity statement and give the scale factor. If not, explain.
Algebra The polygons are similar. Find the value of each variable.
4.5.
6.
Determine whether the triangles are similar. If so, write a similarity statement. If not, explain.
7.
Find the geometric mean of each pair of numbers.
8. 8and129. 20and6
18.A student says that since all isosceles right triangles are similar, all isosceles triangles that are similar must be right triangles. Is the student right? Explain.
6.Theperimeterofarectangleis280cm.Theratioofthewidthtothelengthis 3 : 4. What is the length of the rectangle?
7.The ratio of country albums to jazz albums in a music collection is 2 : 3. If the music collection has 45 albums, how many are country albums?
8.The lengths of the sides of a triangle are in the extended ratio 3 : 6 : 8. The triangle’s perimeter is 510 cm. What are the lengths of the sides?
Algebra Solve each proportion.
29. 30.
In the diagram below, PRQ ~DEF. Find each of the following.
19. thescalefactorofPRQtoDEF
20.mD
21. mR
22.mP
23.DE
24. FE
11.12.