Resources

5.1 - 5.2 QUIZLET

Thanks to Anika :Dave

Here's a Quizlet I made with the terms we've learned so far (Includes location, distance, and definitions)

Link

Chapter Reviews

Thanks to Jaansi, Lekhana & Ishwari

Study Guide & Review

Practice Test

Standardized Test

5.1 - Bisectors of Triangles

Thanks to Ishwari Veerkar

Kuta worksheet, five stars.

Kuta Worksheet #2

MathAids Worksheet

Worksheet #4 (Hard)

5.2 - Medians and Altitudes of a Triangle

Thanks to Ishwari Veerkar

Worksheet #1 (No Answer Key)

Worksheet #2

Kuta Worksheet #3 (Medians)

Kuta Worksheet #4 (Finding the Centroid)

Worksheet #5 (Finding the Circumcenter, Orthocenter & Centroid)

Worksheet #6

5.3 - Inequalities in one Triangle

Thanks to Ishwari Veerkar

Kuta Worksheet #1

Worksheet #2 (Medium)

Worksheet #3 (Hard)

5.5 - Triangle Inequality

Thanks to Ishwari Veerkar

Kuta Software

Worksheet #2 (No Answer Keys)

Worksheet #3 (No Answer Keys)

Kuta Software (5.3 + 5.5)

Worksheet #5

5.1 - 5.5

5.6 - Inequalities in 2 Triangles

Thanks to Ishwari Veerkar & Riya Chowdawarapu

Worksheet #1

Jackpot of Problems!

Another Worksheet

Notes of finding the Centroid, Orthocenter & Circumcenter

Centroid: Averages of the Coordinates

(x1 + x2 + x3) / 3 , (y1 + y2 + y3) / 3

Orthocenter:

1. Find the Perpendicular Slope of the vertices.

2. Plug in the slope and one of the coordinates of the vertices of triangle in a point slope form.

3. After you arrive at 2 separate equations use systems and find the coordinates.

Circumcenter:

1. Find the perpendicular slope of the bisector.

2. Find the midpoint of the segment.

3. Plug in the slope and midpoint in a point slope form.

4. After you arrive at 2 separate equations use systems and find the coordinates.

Notes

5.1

Thanks to Ishwari Veerkar and Thomas Catuosco

Perpendicular Bisector: A segment or a line bisecting a segment at its midpoint and is also perpendicular to that segment.

Perpendicular Bisector Theorem - If line CD is a perpendicular bisector of line AB, then AC=BC.

Converse of the Perpendicular Bisector Theorem - If AE = BE, then E lies on line CD, the perpendicular bisector of line AB>

Concurrent Lines: When 3 or more lines intersect at a common point they are known as concurrent lines.

Point of Concurrency: The point where concurrent lines meet.

Circumcenter Theorem: The point of concurrency of perpendicular bisectors. It can be on the interior, exterior or on the side of the triangle. If point P is the circumcenter of triangle ABC, then PB=PA=PC. Circumcenter is equidistant from all the vertices of the triangle.

Incenter: The point of concurrency of the angle bisectors of a triangle. The incenter is equidistant from all the sides of the triangle.

Angle Bisector Theorem: If ray BF bisects angle DBE, line FD is perpendicular to ray BD, and line FE is perpendicular to ray BE, then DF=FE.

Converse of Angle Bisector Theorem: If line FD is perpendicular to ray BD, line FE is perpendicular to ray BE, and DF=FE, then ray BF bisects angle DBE.

5.2

Thanks to Ishwari Veerkar and Thomas Catuosco

Medians: A segment from a vertex of a triangle to the midpoint of the opposite side

Centroid: The point of concurrency of medians of a triangle.

Centroid Theorem - If point P is the centroid of triangle ABC, then AP=2/3AK, BP=2/3BL, and CP=2/3CJ.

Altitude: A segment from a vertex to the line containing the opposite side and perpendicular to the line containing that side. It can be on the interior, exterior or on the side of the triangle. In short words, altitude means perpendicular height.

Orthocenter: The point of concurrency of the altitudes of a triangle.

5.3

Thanks to Ishwari Veerkar

Exterior Angle Inequality: Measure of an exterior angle of a triangle is greater than the measure of either of its corresponding remote interior angles.

Angle Side Inequality: The longest side of a triangle is always opposite to the largest angle of that triangle. Likewise the shortest side of a triangle is always opposite to the smallest angle of that triangle.

5.5

Thanks to Ishwari Veerkar

Triangle Inequality Theorem: Sum of lengths of any 2 sides of a triangle must be greater than the length of the third side of the triangle.

5.6

Thanks to Ishwari Veerkar

Hinge Theorem: If two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first is larger than the included angle of the second, then the third side of the first triangle is longer than the third side of the second triangle.

Converse of Hinge Theorem: If the two sides of one triangle are congruent to two sides of another triangle, and the third side of the first triangle is greater than the third side of the second triangle, then the included angle of the first triangle is larger than the included angle of the second triangle.