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Transcript
Geometry Guided Notes Triangles Name: ____________________________ Date: ___________________ Period: ____ Corollary – is a theorem that follows from a theorem that ___________________________________ _________________________________________________________________________ A Triangle – 3 sided polygon (3 angles) ∆ - the symbol that represents a triangle; B C Naming a Triangle – each vertex of the triangle will be labeled with a capital letter; use the triangle symbol and each letter to name the triangle; _______________ Parts of a Triangle 4 9 B 3 8 A Interior Angles:___________________ 5 1 Exterior Angles: __________________ 2 6 7 C Vertex (Vertices) – each of the points, _____, ______, ______, is a vertex of the triangle. Adjacent side – two sides that share a common vertex; _________________are adjacent sides Opposite side – the side opposite a specified angle; ̅̅̅̅̅ is opposite ∡_______ Classified by their sides A 1. Equilateral – a triangle with 3 congruent sides C B Corollary for Equilateral Triangles -______________________________________________ __________________________________________________________________________ Geometry Guided Notes Triangles Name: ____________________________ Date: ___________________ Period: ____ 2. Scalene – a triangle that has no congruent sides 3. Isosceles – a triangle with at least 2 congruent sides; an isosceles triangle can have 3 A congruent sides B C Parts of an Isosceles Triangle legs– if a triangle is isosceles with only 2 congruent sides, then the congruent sides are A referred to as the _____________, base - the remaining non-congruent side base angles - ______________________________. C B Base Angles Theorem – If two sides of a triangle are congruent, then ______________ ________________________________________________________________________ Theorem: If two angles of a triangle are congruent, then _______________________ ________________________________________________________________________ Classified by their angles 1. Acute- a triangle with all _________ angles 2. Obtuse – a triangle with exactly _______ __________ angle 3. Equiangular – an acute triangle in which __________________________ Geometry Guided Notes Triangles Name: ____________________________ Date: ___________________ Period: ____ Corollary (Equiangular): If a triangle is equiangular, then it is also _____________________. 4. Right – a triangle with exactly one right angle hypotenuse – if a triangle is a right triangle, then the side opposite the right angle is called the hypotenuse and the sides _________________________________________. ONE 90° ANGLE AND 2 ACUTE ANGLES! Theorem: The acute angles of a right triangle are _______________________________. Example: x 2x Marking the Triangle Equilateral Equiangular Isosceles Scalene Right Geometry Guided Notes Triangles Name: ____________________________ Date: ___________________ Period: ____ Solving Triangles Problems Example #1: ΔABC is an isosceles triangle with ̅̅̅̅ triangle is equilateral. ̅̅̅̅ . Solve for x, then decide if the A 2x - 1 4x - 2 C B x+1 Example #2: Example #3: A A 3x - 5 15 2x + 1 C B B 25 C Triangle Sum Theorem – the sum of the measures of the interior angles of a triangle is __________. Example #1: Find the measure of ∡1, ∡2, and ∡3. 28° 51° 1 42° 2 3 Example #2: Solve for x and find the measure of each angle. 5x + 5 6x 7x - 5 Geometry Guided Notes Triangles Name: ____________________________ Date: ___________________ Period: ____ Example #3: Solve for x. 2x + 3 110° Example #4: Find x and y. 50° y x Exterior Angle Theorem - the measure of an exterior angle of a triangle is equal to the sum of the measures of the __________________________________________________________________ A 1 B C Example #1: A 55° 40° B 1 C Geometry Guided Notes Triangles Name: ____________________________ Date: ___________________ Period: ____ Example #2: A 65° x° 2x + 10 B C Example #3: A 11x - 3 2x + 4 8x + 1 B C Exterior Angle Inequality – the measure of an exterior angle of a triangle is ____________________ the measure of either of the two remote (nonadjacent) interior angles A 1 B C Third Angles Theorem – if two angles of a triangle are _______________ to two angles of second triangle, then the ______________are also ______________________. Geometry Guided Notes Triangles Solve for each missing angle. Name: ____________________________ Date: ___________________ Period: ____