Chapter 5 and Triangle Properties review

Identifying Parts of a Right Triangle Right Angle Leg Leg Hypotenuse

Right Triangle Terms Hypotenuse Legs

Properties of Triangles Triangle Sum Theorem The sum of the measure of the interior angles of a triangle is 180°

Triangle Term Exterior Angle – The angle formed outside the triangle, and along a side as shown Exterior Angle

Triangle Term Exterior Angle – Remote interior angles Exterior Angle

Exterior Angle Theorem The measure of an exterior angle of a triangle is equal to the measure of the two remote interior angles.

Practice Problems

m1=75° m6=40° m2=55° m7=75° m3=55° m8=65° m4=40° m9=115° m5=140°

X=23 Exterior Angle = 100°

Right, Scalene Triangle mA=30° mB=60° mC=90° Right, Scalene Triangle

Isosceles Triangle Properties

Isosceles Triangle Parts An Isosceles triangle has two congruent sides

Isosceles Triangle Conjecture If a triangle is isosceles, then its base angles are congruent

Isosceles Triangle Conjecture If a triangle has two congruent angles then it is an isosceles triangle

Practice Problems

Practice Problems

Practice Problems

Practice Problems

Practice Problems

Practice Problems

Practice Problems

Practice Problems

Practice Problems

Test Yourself on altitudes, medians, bisectors and points of concurrency

Points of Concurrency Type Name Perpendicular Bisectors Circumcenter Angle Bisectors Incenter Medians Centroid Altitudes Orthocenter

Points of Concurrency Properties Type Where Circumcenter Equal distance to vertices Incenter Equal distance to sides Centroid Balancing point 1/3 to side, 2/3 to vertex Orthocenter Nothing special

Points of Concurrency Where they occur Type Where Circumcenter Inside Acute Outside Obtuse On hypotenuse of Right Incenter Inside Triangle Centroid Orthocenter On Right Angle

Name the line Connects the midpoint of a side with a vertex Median

Name the line Bisects the angle of a triangle Angle Bisector

Name the line Through a vertex, forming a right angle with the opposite side Altitude

Name the line From the midpoint of a side, perpendicular to that side Perpendicular Bisector

Name the line The height of the triangle Altitude

Name the line Three of these meet to form the Circumcenter Perpendicular Bisectors

Name the line Three of these meet to form the orthocenter Altitude

Points of Concurrency Type Name Perpendicular Bisectors Circumcenter Angle Bisectors Incenter Medians Centroid Altitudes Orthocenter

Review Concepts

Intersecting points and how they look Vertices Sides Perpendicular Bisectors May not intersect Perpendicular Bisect, Angle Bisectors Bisects Anywhere Medians Starts here Altitudes Perpendicular to May be the side of a triangle itself (right triangle)

Points of Concurrency Type Name Perpendicular Bisectors Circumcenter Angle Bisectors Incenter Medians Centroid Altitudes Orthocenter

Points of Concurrency Where they occur Type Where is it located Circumcenter Inside Acute Outside Obtuse On hypotenuse of Right Incenter Inside Triangle Centroid Orthocenter On Right Angle

Points of Concurrency Superpowers Type Property Circumcenter Equal distance to vertices Incenter Equal distance to sides Centroid Balancing point 1/3 to side, 2/3 to vertex Orthocenter On Euler Line