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Chapter 5 Review

Chapter 5 Review. Segments in Triangles. Test Outline. Multiple Choice Be able to identify vocab (pick out from a picture) Be able to apply SAS and SSS Inequality Theorems (biggest angle across from biggest side)

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Chapter 5 Review

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  1. Chapter 5 Review Segments in Triangles

  2. Test Outline • Multiple Choice • Be able to identify vocab (pick out from a picture) • Be able to apply SAS and SSS Inequality Theorems (biggest angle across from biggest side) • Identify longest/shortest segment and/or largest/smallest angle, also list all sides or angles from least to greatest or greatest to least • Determine if three lengths can be the sides of a triangle

  3. Test Outline Continued • Short Answer/Solving Problems • Be able to use equations that go with centroids, circumcenters, medians, and altitudes to solve problems involving algebra • Be able to list segments and angles from least to greatest in a given triangle

  4. Test Ouline Continued • Indirect Proofs • Be able to write an indirect proof involving two triangles from start to finish • Three step process • 1. assume that …. • 2. then…. This contradicts… • 3. Therefore…

  5. Test Outline Continued • Write and solve inqualities between two triangles • Be able to use the SAS and SSS Inequalities to write and solve inequalities relating the sides or angles of triangles

  6. Practice Problems Points U, V, and W are midpoints of YZ, ZX, and XY. Find a, b, and c. Y 7.4 W U 8.7 5c 3b + 2 15.2 2a Z X V

  7. Practice Problems A.Determine the relationship between the measures of angle ABD and angle DAB B. List the angles of triangle BCD in order from least to greatest A B 5.6 4.8 5.4 5.3 6.4 C 6.1 D 5.2 E

  8. Practice Problems Determine whether the measures 6.8, 7.2, and 5.1 can be lengths of the sides of a triangle.

  9. Practice Problems • Write and inequality relating angle LDM to MDN using the information in the figure. Find a. M 18 16 141 9a + 15 D 12 12 N L

  10. Practice Problems Compare angle WYX and angle ZYW. Write an inequality statement and solve for n. W 11 X 9 8 7n + 5 Z 47 8 Y

  11. Practice Problems In the figure, A is the circumcenter of triangle LMN. Find y if LO=8y + 9, ON=12y – 11 and NP= 10y + 4 L O Q A M N P

  12. Practice Problems In the figure, A is the circumcenter of triangle LMN. Find x if the measure of angle APM= 7x + 13 L O Q A M N P

  13. Practice Problems In triangle RST, RU is an altitude and SV is a median. Find RV if RV=6a + 3 and RT= 10a + 14 R V T S U

  14. Practice Problems Refer to the triangle below, Determine the relationship between lengths of RS and ST. R 62 55 63 T S

  15. Practice Problems Write the assumption you would make to start an indirect proof of the statement: Triangle ABC is congruent to triangle DEF

  16. Practice Problems Can the measures of 5, 7, and 8 be the lengths of the sides of a triangle?

  17. Practice Problems Find the range for the measure of the third side of a triangle if two of its sides measure 4 and 13.

  18. Practice Problem answers: 2(2a)=7.4 2(8.7)=3b+2 2(5c)=15.2 4a=7.4 17.4=3b+2 10c=15.2 a=1.85 b=5.13333 c=1.52

  19. Practice Problem answers: • Angle ABD > angle DAB • Angle D < angle C < angle B

  20. Practice Problem answers: 5.1 + 6.8 = 11.9 11.9>7.2 Yes, because the sum of the two smallest sides is greater than the third side.

  21. Practice Problem answers: Angle LDM > Angle MDN 141>9a+15 a<14

  22. Practice Problem answers: Angle WYX > Angle ZYW 7n+15>47 n>6

  23. Practice Problem answers: Perpendicular bisectors split the opposite side into 2 congruent segments 8y+9=12y-11 y=5

  24. Practice Problem answers: Perpendicular bisectors make right angles with the opposite side 7x+13=90 x=11

  25. Practice Problem answers: Medians go to the midpoint which splits the opposite side into 2 congruent segments 2(6a+3)=10a+14 12a +6=10a+14 a=4

  26. Practice Problem answers: Assume that triangle ABC is not congruent to triangle DEF.

  27. Practice Problem answers: 5+7=12 12>8 Yes, because the sum of the two smallest sides is greater than the third side.

  28. Practice Problem answers: 13-4<x<13+4 9<x<17

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