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# Triangles

Intro to Triangles

by

Tweet## Michelle Palker

on 26 October 2012#### Transcript of Triangles

Intro to Triangles 10.23.12 ANGLES Classify a Triangle by its if ALL 3 Angles are less than 90 Degrees,

then we have an ACUTE TRIANGLE ACUTE 81 54 45 If ONE angle is 90 degrees,

than we have a RIGHT TRIANGLE RIGHT 90 47 43 If ONE angle is over 90 degrees, than

we have an OBTUSE TRIANGLE OBTUSE 101 24 55 If ALL 3 angles are equal, than it is an

EQUIANGULAR TRIANGLE EQUIANGULAR 60 60 60 SIDES Classify a Triangle by its If ALL 3 sides are Congruent, then it is an

EQUILATERAL TRIANGLE EQUILATERAL 8 8 8 If 2 sides are congruent, then

it is an ISOSCELES TRIANGLE ISOSCELES 12 12 16 If NO sides are congruent, then it

is a SCALENE TRIANGLE SCALENE 3.5 1.2 7.9 What type of Triangle am I? 6 7 6 T S U 27 28 125 o o o M A P MAP: STU: 78 67 35 o o o NEW N E W The SUM of all 3 angles of a

Triangle = 180 Degrees TRIANGLE ANGLE

SUM THEOREM A B C m A+ m B+ m C =180 Find the Missing Angle Measure 22 x y 81 42 x HOW DO WE KNOW IF

WE HAVE A TRIANGLE? TRIANGLE INEQUALITY THEOREM when you add 2 sides of a triangle together, the sum will be GREATER than the third side A B C A+B>C

B+C>A

C+A>B Do these side lengths form a triangle or not? Justify 3 8 7 1.5, 8.1 ,9.8 Can a triangle have sides with the

indicated length? Justify 2, 7, 9 Two sides of a triangle have lengths 8cm

and 10 cm. What are the possible lengths

for the third side? The LARGEST ANGLE is always across from the LARGEST SIDE Relationship of sides

to angles The MEDIUM ANGLE is always

across from the MEDIUM SIDE The SMALLEST ANGLE is always across from the SMALLEST SIDE 20 40 120 22.7 3.4 13.9 List the angles from Smallest to Largest 8 6 5 R U F List the angles from Smallest to Largest 86.5 100.2 68.5 M A P List the Sides from Shortest to Longest 103 33 44 o o o C R Y o o o Example #1 Example #2 Example #3 Example #1 Example #2 Example #3 Example #4 List the sides from Shortest to Longest T U E 64 61 o o Worksheet 5.1 Triangles HOMEWORK Example #1 33 98 24 Example #2 Example #3 Example #4 Note Time! ... small Note: Add the 2 smallest #'s Ex#1 Ex#2 4 2 1 Exterior Angles of

a Triangle 4 2 1 Exterior Angle 3 3 Each Exterior Angle of a Triangle has 2 remote interior angles What do we know about

angles of a Triangle? 1 2 3 4 The measure of each exterior angle equals the

sum of its 2 remote interior angles Triangle Exterior

Angle Theorem 1 2 3 4 <4 = <1 + <2 Find the Value of X Example #1 x 40 30 Example #2 X 125 33 note: The remote interior angles do not

touch the Exterior Angle Example #3 134 134 o (2x+8) 18 Name the Remote

Interior Angles of each Exterior Angle 1 2 3 4 5 6 CLASSWORK-->HOMEWORK

Worksheet:

Exterior Angle Theorem

ODDS STUDY FOR YOUR QUIZ TOMORROW!!!! Example #4 Work on Warm up for TODAY

Take out your Homework from yesterday for stamping!

Have your notebook out for NOTE TAKING Thursday 10/25/12 If 2 sides of a triangle are congruent, then the angles opposite them are congruent. Isosceles Triangles Isosceles Triangle Theorem A B C <A = <B ~ Converse of Isosceles Triangle Theorem If 2 angles of a triangle are congruent,

then the two opposite sides are congruent A B C CA =BC ~ If a triangle is equilateral, then the

triangle is equiangular EQUILATERAL TRIANGLES X Y Z If a triangle is equiangular, then

the triangle is equilateral X Y Z

Full transcriptthen we have an ACUTE TRIANGLE ACUTE 81 54 45 If ONE angle is 90 degrees,

than we have a RIGHT TRIANGLE RIGHT 90 47 43 If ONE angle is over 90 degrees, than

we have an OBTUSE TRIANGLE OBTUSE 101 24 55 If ALL 3 angles are equal, than it is an

EQUIANGULAR TRIANGLE EQUIANGULAR 60 60 60 SIDES Classify a Triangle by its If ALL 3 sides are Congruent, then it is an

EQUILATERAL TRIANGLE EQUILATERAL 8 8 8 If 2 sides are congruent, then

it is an ISOSCELES TRIANGLE ISOSCELES 12 12 16 If NO sides are congruent, then it

is a SCALENE TRIANGLE SCALENE 3.5 1.2 7.9 What type of Triangle am I? 6 7 6 T S U 27 28 125 o o o M A P MAP: STU: 78 67 35 o o o NEW N E W The SUM of all 3 angles of a

Triangle = 180 Degrees TRIANGLE ANGLE

SUM THEOREM A B C m A+ m B+ m C =180 Find the Missing Angle Measure 22 x y 81 42 x HOW DO WE KNOW IF

WE HAVE A TRIANGLE? TRIANGLE INEQUALITY THEOREM when you add 2 sides of a triangle together, the sum will be GREATER than the third side A B C A+B>C

B+C>A

C+A>B Do these side lengths form a triangle or not? Justify 3 8 7 1.5, 8.1 ,9.8 Can a triangle have sides with the

indicated length? Justify 2, 7, 9 Two sides of a triangle have lengths 8cm

and 10 cm. What are the possible lengths

for the third side? The LARGEST ANGLE is always across from the LARGEST SIDE Relationship of sides

to angles The MEDIUM ANGLE is always

across from the MEDIUM SIDE The SMALLEST ANGLE is always across from the SMALLEST SIDE 20 40 120 22.7 3.4 13.9 List the angles from Smallest to Largest 8 6 5 R U F List the angles from Smallest to Largest 86.5 100.2 68.5 M A P List the Sides from Shortest to Longest 103 33 44 o o o C R Y o o o Example #1 Example #2 Example #3 Example #1 Example #2 Example #3 Example #4 List the sides from Shortest to Longest T U E 64 61 o o Worksheet 5.1 Triangles HOMEWORK Example #1 33 98 24 Example #2 Example #3 Example #4 Note Time! ... small Note: Add the 2 smallest #'s Ex#1 Ex#2 4 2 1 Exterior Angles of

a Triangle 4 2 1 Exterior Angle 3 3 Each Exterior Angle of a Triangle has 2 remote interior angles What do we know about

angles of a Triangle? 1 2 3 4 The measure of each exterior angle equals the

sum of its 2 remote interior angles Triangle Exterior

Angle Theorem 1 2 3 4 <4 = <1 + <2 Find the Value of X Example #1 x 40 30 Example #2 X 125 33 note: The remote interior angles do not

touch the Exterior Angle Example #3 134 134 o (2x+8) 18 Name the Remote

Interior Angles of each Exterior Angle 1 2 3 4 5 6 CLASSWORK-->HOMEWORK

Worksheet:

Exterior Angle Theorem

ODDS STUDY FOR YOUR QUIZ TOMORROW!!!! Example #4 Work on Warm up for TODAY

Take out your Homework from yesterday for stamping!

Have your notebook out for NOTE TAKING Thursday 10/25/12 If 2 sides of a triangle are congruent, then the angles opposite them are congruent. Isosceles Triangles Isosceles Triangle Theorem A B C <A = <B ~ Converse of Isosceles Triangle Theorem If 2 angles of a triangle are congruent,

then the two opposite sides are congruent A B C CA =BC ~ If a triangle is equilateral, then the

triangle is equiangular EQUILATERAL TRIANGLES X Y Z If a triangle is equiangular, then

the triangle is equilateral X Y Z