We spent some time going over the review from Friday and answering questions that the students had. We also went through 2 more inequality proofs together before getting started on the 2nd of our reviews in getting ready for the chapter 6 test.
Assignment: Chapter 6 Review #2
Ch. 6 Test tomorrow
Test 24 ; Chapter 6 Test
1. false
2. true
3. true
4. false
5. true
6. a. If pts. X, Y, and Z are noncollinear, then XY + YZ does not equal XZ
b. If XY + YZ does not equal XZ, then pts. X, Y, and Z are noncollinear.
c. XY + YZ does not equal XZ
7. less than
8. greater than
9. greater than
10. equal
11. less than
12. less than, greater than
13. greater than
14. equal
15. greater than
16. angle L
17. segment NO
18. a. HF
b. SAS inequality theorem
19. a. FG
b. Longer side is opposite the larger angle (triangle inequality theorem)
20. a. HF
b. longer side is opposite the larger angle (triangle inequality theorem)
21. statements reasons
angle 1 > angle DBC ext. angle is greater than either remote int. angle
DC congruent to BC given
angle BDC cong. angle DBC isos. triangle theorem
angle 1 > angle BDC substitution
Inequality Proofs
1. statements reasons
angle C > angle A given
angle D > angle B given
AE > CE longer side is opposite larger angle in triangles
BE > DE longer side is opposite larger angle in triangles
AE + EB = AB segment addition postulate
CE + ED = CD segment addition postulate
AB > CD property of inequality
2. don't do this proof
3. statements reasons
angle 1 less than angle 3 given
BA parallel to CD given
AC > AD given
angle 3 congruent angle 2 if lines parallel, then AIA congruent
angle 1 < angle 2 substitution
BC > AC longer side is opposite larger angle in triangle
BC > AD subst. / transitive
4. statements reasons
AC bisects angle BAD given
angle 1 congruent to angle 2 def. of bisect
angle 3 = angle B + angle 1 ext. angle = sum of remote int. angles
angle 3 > angle 1 property of inequality
angle 3 > angle 2 substitution
AD > CD longest side is opposite largest angle in triangle
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