5 Chapter Review

Connecting BIG ideas and Answering the Essential Questions

1 Coordinate Geometry Use parallel and perpendicular lines, and the slope, midpoint, and distance formulas to find intersection points and unknown lengths.	Midsegments of Triangles (Lesson 5-1) If D E ¯ d e bar  is a midsegment, then A C ¯ ║ D E ¯ eh c bar , box drawings double vertical , d e bar  and D E = 1 2 A C . d e equals . 1 half eh c .
2 Measurement Use theorems about perpendicular bisectors, angle bisectors, medians, and altitudes to find points of concurrency, angle measures, and segment lengths.	Concurrent Lines and Segments in Triangles (Lessons 5-2, 5-3, and 5-4) Concurrent Lines and Segments Intersection perpendicular bisectors angle bisectors medians lines containing altitudes circumcenter incenter centroid orthocenter
3 Reasoning and Proof You can write an indirect proof by showing that a temporary assumption is false.	Indirect Proof (Lesson 5-5) Assume temporarily the opposite of what you want to prove. Show that this temporary assumption leads to a contradiction. Conclude that what you want to prove is true.	Inequalities in Triangles (Lessons 5-6 and 5-7) Use indirect reasoning to prove that the longer of two sides of a triangle lies opposite the larger angle, and to prove the Converse of the Hinge Theorem.

Chapter Vocabulary

• altitude of a triangle (p. 310)
• centroid of a triangle (p. 309)
• circumcenter of a triangle (p. 301)
• circumscribed about (p. 301)
• concurrent (p. 301)
• distance from a point to a line (p. 294)
• equidistant (p. 292)
• incenter of a triangle (p. 303)
• indirect proof (p. 317)
• indirect reasoning (p. 317)
• inscribed in (p. 303)
• median of a triangle (p. 309)
• midsegment of a triangle (p. 285)
• orthocenter of a triangle (p. 311)
• point of concurrency (p. 301)

Choose the correct vocabulary term to complete each sentence.

1. A (centroid, median) of a triangle is a segment from a vertex of the triangle to the midpoint of the side opposite the vertex.
2. The length of the perpendicular segment from a point to a line is the (midsegment, distance from a point to the line).
3. The (circumcenter, incenter) of a triangle is the point of concurrency of the angle bisectors of the triangle.

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