Triangles and Angles Students will classify triangles by their sides and by their angles. Students...

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Triangles and Angles • Students will classify triangles by their sides and by their angles. • Students will apply the Triangle-Angle Sum Theorem, the Isosceles Triangle Theorem and its converse, linear pair, vertical angles and the Exterior Angle Theorem

Transcript of Triangles and Angles Students will classify triangles by their sides and by their angles. Students...

Page 1: Triangles and Angles Students will classify triangles by their sides and by their angles. Students will apply the Triangle-Angle Sum Theorem, the Isosceles.

Triangles and Angles • Students will classify triangles by their sides and by their angles.

• Students will apply the Triangle-Angle Sum Theorem, the Isosceles Triangle Theorem and its converse, linear pair, vertical angles and the Exterior Angle Theorem

Page 2: Triangles and Angles Students will classify triangles by their sides and by their angles. Students will apply the Triangle-Angle Sum Theorem, the Isosceles.

Types of TrianglesClassifying by Side:

• Equilateral - 3 congruent sides

• Isosceles - at least 2 congruent sides

• Scalene - no congruent sides

leg leg

base

Page 3: Triangles and Angles Students will classify triangles by their sides and by their angles. Students will apply the Triangle-Angle Sum Theorem, the Isosceles.

Classifying by Angle:• Acute - 3 acute angles

• Equiangular - 3 congruent angles

• Right - 1 right angle

• Obtuse - 1 obtuse angle

leg

leg

hypotenuse

Page 4: Triangles and Angles Students will classify triangles by their sides and by their angles. Students will apply the Triangle-Angle Sum Theorem, the Isosceles.

More Vocabulary• Interior Angles The three original angles of the

triangle.

• Exterior Angles The angles that are adjacent to the

interior angles of the triangle.

• Theorem 4.1 Triangle Sum Theorem

The sum of the measures of the interior angles of a triangle is 1800.

mA + mB + mC = 1800

A

BC

1

2

3

1

2

3

Page 5: Triangles and Angles Students will classify triangles by their sides and by their angles. Students will apply the Triangle-Angle Sum Theorem, the Isosceles.

• Corollary to the Triangle Sum Theorem

The acute angles of a right triangle are complementary.

mA + mB = 900

A

CB

Page 6: Triangles and Angles Students will classify triangles by their sides and by their angles. Students will apply the Triangle-Angle Sum Theorem, the Isosceles.

• Exterior Angle Theorem The measure of an exterior angle of a

triangle is equal to the sum of the measures of the two nonadjacent interior angles.

mCBD = mA + mC

A

C

1

B D

Page 7: Triangles and Angles Students will classify triangles by their sides and by their angles. Students will apply the Triangle-Angle Sum Theorem, the Isosceles.

Vertical Angles Conjecture• You will need: a straight edge, patty paper

1. Draw two intersecting lines onto patty paper. Label the angles as shown. Which angles are vertical angles?

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Page 8: Triangles and Angles Students will classify triangles by their sides and by their angles. Students will apply the Triangle-Angle Sum Theorem, the Isosceles.

2. Fold the paper so that the vertical angles lie over each other. What do you notice about their measures?

3. Fold the paper so that the other pair of vertical angles lie over each other. What do you notice about their measures?

4. Compare the results with the results of others. Complete the statement.

Vertical Angles Conjecture:If two angles are vertical angles, then ______________.they are congruent

Page 9: Triangles and Angles Students will classify triangles by their sides and by their angles. Students will apply the Triangle-Angle Sum Theorem, the Isosceles.

Linear Pair ConjectureUsing the previous figure – measure the 4 indicated

angles with a protractor.

What do you notice about the sum of the two adjacent angles (linear pair)?

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If two angles form a linear pair, then _____________________________________.the measures of the angles add up to 180o

Page 10: Triangles and Angles Students will classify triangles by their sides and by their angles. Students will apply the Triangle-Angle Sum Theorem, the Isosceles.

Find the value of x.1. 2.

FE

x = 6x = 11

Page 11: Triangles and Angles Students will classify triangles by their sides and by their angles. Students will apply the Triangle-Angle Sum Theorem, the Isosceles.

Find the measures of the missing angles

60o

55o

65o

acb

d

feh i

g

a=60o

b=120o

c=120o

d=115o

e=65o

f=115o

g=125o

h=55o

i=125o