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Chapter 5 and Triangle Properties review
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Identifying Parts of a Right Triangle
Right Angle Leg Leg Hypotenuse
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Right Triangle Terms Hypotenuse Legs
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Properties of Triangles
Triangle Sum Theorem The sum of the measure of the interior angles of a triangle is 180°
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Triangle Term Exterior Angle – The angle formed outside the triangle, and along a side as shown Exterior Angle
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Triangle Term Exterior Angle – Remote interior angles Exterior Angle
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Exterior Angle Theorem
The measure of an exterior angle of a triangle is equal to the measure of the two remote interior angles.
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Practice Problems
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m1=75° m6=40° m2=55° m7=75° m3=55° m8=65° m4=40° m9=115° m5=140°
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X=23 Exterior Angle = 100°
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Right, Scalene Triangle
mA=30° mB=60° mC=90° Right, Scalene Triangle
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Isosceles Triangle Properties
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Isosceles Triangle Parts
An Isosceles triangle has two congruent sides
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Isosceles Triangle Conjecture
If a triangle is isosceles, then its base angles are congruent
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Isosceles Triangle Conjecture
If a triangle has two congruent angles then it is an isosceles triangle
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Practice Problems
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Practice Problems
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Practice Problems
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Practice Problems
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Practice Problems
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Practice Problems
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Practice Problems
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Practice Problems
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Practice Problems
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Test Yourself on altitudes, medians, bisectors and points of concurrency
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Points of Concurrency Type Name Perpendicular Bisectors Circumcenter
Angle Bisectors Incenter Medians Centroid Altitudes Orthocenter
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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
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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
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Name the line Connects the midpoint of a side with a vertex Median
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Name the line Bisects the angle of a triangle Angle Bisector
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Name the line Through a vertex, forming a right angle with the opposite side Altitude
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Name the line From the midpoint of a side, perpendicular to that side
Perpendicular Bisector
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Name the line The height of the triangle Altitude
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Name the line Three of these meet to form the Circumcenter
Perpendicular Bisectors
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Name the line Three of these meet to form the orthocenter Altitude
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Points of Concurrency Type Name Perpendicular Bisectors Circumcenter
Angle Bisectors Incenter Medians Centroid Altitudes Orthocenter
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Review Concepts
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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)
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Points of Concurrency Type Name Perpendicular Bisectors Circumcenter
Angle Bisectors Incenter Medians Centroid Altitudes Orthocenter
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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
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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
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