Section 5. 3: Use Angle Bisectors in Triangles Section 5 Section 5.3: Use Angle Bisectors in Triangles Section 5.4: Use Medians and Altitudes

Section 5.3: Use Angle Bisectors in Triangles Vocabulary: Angle bisector - divides an angle into two congruent adjacent angles Incenter – where all of the angle bisectors of a triangle intersect. The incenter is equidistant from all of the sides of the triangle.

Section 5.3: Use Angle Bisectors in Triangles Theorems: Angle Bisector Theorem If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle Converse of the Angle Bisector Theorem If a point is equidistant from the sides of the angle, then it is on the angle bisector Concurrency of Angle Bisectors of a Triangle The angle bisectors intersect at a point that is equidistant from all sides of the triangle (incenter)

Section 5.3: Use Angle Bisectors in Triangles Things to remember: The angles cut by the angle bisector are congruent The distance from the incenter to any side of the triangle is the same Use the Pythagorean Theorem as needed to find any missing lengths Practice problems: Workbook Pg 289 # 1 - 10

Section 5.4: Use Medians and Altitudes Vocabulary: Median of a triangle – segment from a vertex to the midpoint of the side opposite Centroid – where all of the medians of a triangle intersect (ALWAYS inside the triangle) Altitude of a triangle – perpendicular segment from a vertex to the opposite side (or the line that contains the opposite side) Orthocenter – where all of the altitudes of a triangle intersect (may be inside or outside the triangle)

Section 5.4: Use Medians and Altitudes Theorems: Concurrency of the Medians of a Triangle The medians of a triangle intersect at a point that is two-thirds of the distance from each vertex to the midpoint of the opposite side (centroid) Concurrency of the Altitudes of a Triangle The altitudes of a triangle intersect at a point (orthocenter)

Section 5.4: Use Medians and Altitudes Things to remember: Medians cut opposite side into congruent segments Altitudes MUST be perpendicular to the side opposite (or the line containing the side…extend the side out for obtuse triangles) Centroid is 2/3 of the distance from the vertex and 1/3 of the distance from the side Practice problems: Workbook Pg 294 # 1 - 16

What is coming up… Thurs 3/5 Wednesday 3/11 Fri 3/6 Thursday 3/12 Sections 5.7, 5.8, and 5.9 Work on task in class Fri 3/6 Thursday 3/12 Sections 5.10, 5.11, and 5.12 Review for Ch 5 Test Monday 3/9 Friday 3/13 Review for Benchmark Ch 5 Test Tuesday 3/10 3rd Quarter Benchmark

Homework (in your book…) Section 5.3 Page 274 # 1 – 12 and # 14 – 17 Section 5.4 Page 280 # 1 – 6 and # 10 - 24