Chapter 5 Semester Review Name: _________________________________

Please answer all questions and show ALL work for multi-step problems.

5.1 Perpendicular and Angle Bisectors

Example 1: Example 2:

Given that AD is the perpendicular bisector Given that m TSV 37 , find m UST.

of BC , AB=4.5, AC=4.5, and DC=6.5, find BC.

Example 3: Example 4:

Given that AD is the perpendicular bisector Given that m USV 4x 18 and

of BC , AB = 4a + 2, and AC = 6a – 24, identify AC. m VST 7x 12 , find the m UST.

5.2-5.3 Points of Concurrency

Example 1: DG, EG, and FG are the perpendicular Example 2: GJ and IJ are the angle bisectors of bisectors of ∆ABC . Find all possible GIH. side lengths

Part 1: Find KGJ , GIH , GIJ , and GJK

Part 2: Find the distance from J to GH. _______________

Find the distance from J to IH. _______________

Example 3: In ∆ABC, AE = 18, DG = 11, and

BG = 10. Find all possible side lengths.

5.4 Midsegment Theorem

Use the diagram below to answer Examples 2-5. HG and HI are midsegments of the triangle.

Example 1: HI

Example 2: FD

Example 3: mFIH

Example 4: GD

5.5 Inequalities in One Triangle Example 1: Name the angles in order Example 2: Name the sides in order

from smallest to largest. from smallest to largest.

For examples 1 and 2, tell whether a triangle can have sides with the given lengths. Explain why or why

not.

Example 1: Example 2:

7, 11, 18 3, 7, 9

Example 3: If d = 17 and e = 25, what are the possible lengths for side f?

5.6 Inequalities in Two Triangle

Compare the given measures.

Example 1: AB and DE Example 2: mI and mL

Find the range of values for x.

Example 3: